From 10c79cb47ce9c2af4739e7575b2dfe4c960bd5b7 Mon Sep 17 00:00:00 2001 From: maria Date: Thu, 22 Jul 2021 23:24:13 +0200 Subject: [PATCH] saving results to file --- gaknot/__init__.py | 42 +- gaknot/cable_signature.sage | 127 +- gaknot/main.sage | 286 +- gaknot/signature.sage | 22 +- gaknot/utility.py | 4 +- notebooks/lemma.ipynb | 99 + notebooks/main.ipynb | 268137 --------------------------------- notebooks/tests.ipynb | 287 +- 8 files changed, 573 insertions(+), 268431 deletions(-) create mode 100644 notebooks/lemma.ipynb delete mode 100644 notebooks/main.ipynb diff --git a/gaknot/__init__.py b/gaknot/__init__.py index c3e5972..bbf15c9 100644 --- a/gaknot/__init__.py +++ b/gaknot/__init__.py @@ -6,27 +6,33 @@ r"""calculations of signature function and sigma invariant of generalized algebr The package was used to prove Lemma 3.2 from a paper 'On the slice genus of generalized algebraic knots' Maria Marchwicka and Wojciech Politarczyk). It contains the following submodules. - 1) signature.sage - contains SignatureFunction class; + 1) main.sage - with function prove_lemma + 2) signature.sage - contains SignatureFunction class; it encodes twisted and untwisted signature functions of knots and allows to perform algebraic operations on them. - 2) cable_signature.sage - contains the following classes: + 3) cable_signature.sage - contains the following classes: a) CableSummand - it represents a single cable knot, b) CableSum - it represents a cable sum, i. e. linear combination of single cable knots; since the signature function and sigma invariant are additive under connected sum, the class use calculations from CableSummand objects, - c) CableTemplate - it represents schema for a cable sums. - 3) main.sage - module that encodes interesting schemas for cable and perform calculations, - e.g. a proof for Lemma 3.2 from the paper. + c) CableTemplate - it represents a scheme for a cable sums. + """ -# -# A knot (cable sum) is encoded as a list where each element (also a list) corresponds to a cable knot, e.g. a list -# [[1, 3], [2], [-1, -2], [-3]] encodes -# T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7). -# -# To calculate the number of characters for which signature function vanish use -# the function . -# + +from .utility import import_sage +import os + +package = __name__.split('.')[0] +dirname = os.path.dirname +path = dirname(dirname(__file__)) +import_sage('signature', package=package, path=path) +import_sage('cable_signature', package=package, path=path) +import_sage('main', package=package, path=path) + +from .main import prove_lemma + + # EXAMPLES:: # # sage: eval_cable_for_null_signature([[1, 3], [2], [-1, -2], [-3]]) @@ -56,13 +62,3 @@ It contains the following submodules. # 2) set each q_i all or choose range in which q_i should varry # 3) choose vector v / theta vector. # - -from .utility import import_sage -import os - -package = __name__.split('.')[0] -dirname = os.path.dirname -path = dirname(dirname(__file__)) -import_sage('signature', package=package, path=path) -import_sage('cable_signature', package=package, path=path) -import_sage('main', package=package, path=path) diff --git a/gaknot/cable_signature.sage b/gaknot/cable_signature.sage index 221caa1..2cf220d 100644 --- a/gaknot/cable_signature.sage +++ b/gaknot/cable_signature.sage @@ -3,7 +3,9 @@ import numpy as np import itertools as it import warnings +import logging import re +import ast from typing import Iterable from collections import Counter from sage.arith.functions import LCM_list @@ -487,8 +489,11 @@ class CableSum: return result.is_integer() def is_function_big_in_ranges(self, ranges_list, invariant=SIGMA, - verbose=None): + verbose=None, details=False, + p_part_order=None): verbose = verbose or self.verbose + p_part_order = p_part_order or self.q_order + if invariant == SIGNATURE: get_invariant = self.get_sign_ext_for_theta name = "signature (extremum)" @@ -496,21 +501,25 @@ class CableSum: get_invariant = self.sigma_as_function_of_theta name = "sigma value" + if verbose: + msg = "\nCalculating {}-primary part.".format(p_part_order) + print(msg) + + logging.info(str(ranges_list)) + + for thetas in it.product(*ranges_list): # Check only non-zero metabolizers. if not self.is_metabolizer(thetas) or not any(thetas): continue - # - # cond1 = thetas[0] and thetas[3] and not thetas[1] and not thetas[2] - # cond = thetas[0] and thetas[3] and not thetas[1] and not thetas[2] - function_is_small = True # Check if any element generated by thetas vector # has a large signature or sigma. - for shift in range(1, self.q_order): - shifted_thetas = [shift * th for th in thetas] + for shift in range(1, p_part_order): + shifted_thetas = \ + [(shift * th) % p_part_order for th in thetas] limit = 5 + np.count_nonzero(shifted_thetas) inv_value = get_invariant(shifted_thetas, limit=limit) abs_value = abs(inv_value) @@ -518,17 +527,22 @@ class CableSum: if verbose: if shift == 1: print("\n" + "*" * 10) - print("Knot sum:\n" + self.knot_description) - print("[ characters ] " + name) + print("[ character ] " + name) print(shifted_thetas, end=" ") print(inv_value) if abs_value > limit: function_is_small = False - if invariant == SIGMA and verbose: + if details: self.print_calculations_for_sigma(*shifted_thetas) break if function_is_small: + if verbose and invariant == SIGMA: + msg = "For an element x = " + str(thetas) + msg += " there does not exist any shift such that " + msg += "|sigma(K, shift * x)| > {}.\n".format(limit) + msg += "We can not give any lower bound for 4-genus." + print(msg) return False return True @@ -569,34 +583,63 @@ class CableSum: print("Sigma = {} ~ {}\n".format(sigma[2], int(sigma[2]))) # function that proves the main lemma - def is_function_big_for_all_metabolizers(self, invariant=SIGMA): + def is_function_big_for_all_metabolizers(self, invariant=SIGMA, + verbose=False, details=False): + logging.info("start of is_function_big_for_all_metabolizers") + if invariant == SIGNATURE: + name = "signature (extremum)" + else: + name = "sigma value" + num_of_summands = len(self.knot_sum_as_k_valus) if num_of_summands % 4: f_name = self.is_signature_big_for_all_metabolizers.__name__ msg = "Function {}".format(f_name) + " is implemented only for " +\ "knots that are direct sums of 4n direct summands." raise ValueError(msg) + # check each p-primary part separately + logging.info("number of summands is {}".format(num_of_summands)) for shift in range(0, num_of_summands, 4): - # set character (twist) to be zero for all summands - ranges_list = num_of_summands * [range(0, 1)] + + logging.info("shift is {}".format(shift)) + p_part_order = 2 * self.patt_k_list[shift] + 1 + + logging.info("set character (twist) to be zero for all summands") + ranges_list = num_of_summands * [range(1)] + logging.info(str(ranges_list)) + + # change ranges for all but one character for current p-primary part - ranges_list[shift : shift + 3] = \ - [range(0, i + 1) for i in self.patt_k_list[shift: shift + 3]] - # change range for last character in current p-primary part + ranges_list[shift + 1 : shift + 4] = 3 * [range(p_part_order)] + + # change range for first character in current p-primary part # this one is consider to be 0 or 1 - # For any characters combinations (vectors) [a_1, a_2, a_3, a_4] where a_4 != 0 - # exists such as k < p that k * a_4 % p == 1. - ranges_list[shift + 3] = range(0, 2) - if not self.is_function_big_in_ranges(ranges_list, invariant): + # For any characters combinations (vectors) [a_1, a_2, a_3, a_4] + # where a_4 != 0 exists such a k < p that k * a_1 % p == 1. + ranges_list[shift] = range(0, 2) + logging.info("\n\ncall is_function_big_in_ranges with values") + logging.info(str(ranges_list)) + + if not self.is_function_big_in_ranges(ranges_list, invariant, + p_part_order=p_part_order, + verbose=verbose, + details=details): + logging.info("Not proven.") return False + if verbose and invariant == SIGMA: + msg = "For each p-primery part for each vector x there exist " + msg += "a number 0 < shift < p such that " + msg += "sigma(K, shift * x) > 5 + eta(K, shift * x)." + print(msg) + print("q.e.d.") return True class CableTemplate: def __init__(self, knot_formula, q_vector=None, k_vector=None, - generate_q_vector=True, slice=True, verbose=False): + generate_q_vector=True, algebraic=True, verbose=False): self.verbose = verbose self._knot_formula = knot_formula # q_i = 2 * k_i + 1 @@ -605,7 +648,27 @@ class CableTemplate: elif q_vector is not None: self.q_vector = q_vector elif generate_q_vector: - self.q_vector = self.get_q_vector(slice=slice) + self.q_vector = self.get_q_vector(algebraic=slice) + self.templete_description = self.get_template_descrption() + + + def __str__(self): + return self.templete_description + + def get_template_descrption(self): + k_indices = re.sub(r'[k ]', '', self.knot_formula) + k_indices = re.sub(r'\[\d+\]', lambda x: x.group()[1:-1], k_indices) + k_indices = ast.literal_eval(k_indices) + description = "" + for summand in k_indices : + part = "" + if summand[0] < 0: + part += "-" + part += "T(" + for k in summand: + part += "2, q_" + str(abs(k)) + "; " + description += part[:-2] + ") # " + return description[:-3] @property def cable(self): @@ -616,7 +679,7 @@ class CableTemplate: self.fill_q_vector() return self._cable - def fill_q_vector(self, q_vector=None, slice=True, lowest_number=2): + def fill_q_vector(self, q_vector=None, algebraic=True, lowest_number=2): self.q_vector = q_vector or self.get_q_vector(slice, lowest_number) @property @@ -631,6 +694,7 @@ class CableTemplate: self._k_vector = k if self.extract_max(self.knot_formula) > len(k) - 1: msg = "The vector for knot_formula evaluation is to short!" + msg += "Note that we count from 0 (not 1)." msg += "\nk_vector " + str(k) + " \nknot_formula " \ + str(self.knot_formula) raise IndexError(msg) @@ -652,19 +716,28 @@ class CableTemplate: numbers = map(int, numbers) return max(numbers) - def get_q_vector(self, slice=True, lowest_number=2): + def get_q_vector(self, algebraic=True, lowest_number=2): + r""" + Returns q-vector with certain properties. + + If slice a specific relation for each cabling-level is preserved. + Consider a cable T(2, q_0; 2, q_1; ...; 2, q_n). + Then for every q_i, q_(i + 1): q_(i + 1) > q_i * 4 + """ knot_formula = self.knot_formula q_vector = [0] * (self.extract_max(knot_formula) + 1) P = Primes() - for layer in self.get_layers_from_formula(knot_formula)[::-1]: + for layer in self._get_layers_from_formula(knot_formula)[::-1]: for el in layer: q_vector[el] = P.next(lowest_number) lowest_number = q_vector[el] - lowest_number *= 4 + if slice: + lowest_number *= 4 return q_vector @staticmethod - def get_layers_from_formula(knot_formula): + def _get_layers_from_formula(knot_formula): + r"""helper method for get_q_vector""" k_indices = re.sub(r'[k-]', '', knot_formula) k_indices = re.sub(r'\[\d+\]', lambda x: x.group()[1:-1], k_indices) k_indices = eval(k_indices) diff --git a/gaknot/main.sage b/gaknot/main.sage index 30ccec6..2e48332 100644 --- a/gaknot/main.sage +++ b/gaknot/main.sage @@ -1,6 +1,9 @@ #!/usr/bin/env sage -python -# TBD: read about Factory Method, variable in docstring, sage documentation, + +# TBD +# print scheme and knot nicely +# read about Factory Method, variable in docstring, sage documentation, # print calc. to output file # decide about printing option # make __main__? @@ -13,6 +16,9 @@ import re import numpy as np import importlib +# constants - which invariants should be calculate +SIGMA = 0 +SIGNATURE = 1 if __name__ == '__main__': from utility import import_sage @@ -33,41 +39,62 @@ cs = import_sage('cable_signature', package=package, path=path) # def __init__(self): # self.f_results = os.path.join(os.getcwd(), "results.out") -class Schemas: +class Schema: + r"""This class stores inreresting schema of cable sums. + Cable knots sum can be given as a scheme, e.g. a scheme from the paper: + K(p_1 , p_2 , q_1 , q_2 , q_3 ) = + T(2, q_1; 2, p_1) # -T(2, q_2; 2, p_1) # T(2, p_1) # -T(2, q_3; 2, p_1) + + T(2, q_2; 2, p_2) # -T(2, p_2) # T(2, q_3; 2, p_2) # -T(2, q_1; 2, p_2). + We can represent it as nested list: + lemma_scheme = "[[ k[5], k[3]], " + \ + "[ -k[1], -k[3]], " + \ + "[ k[3]], " + \ + "[ -k[6], -k[3]], " + \ + "[ k[1], k[7]], " + \ + "[ -k[7]], " + \ + "[ k[6], k[7]], " + \ + "[ -k[5], -k[7]]]", + where each k[i] corresponds to some q_i or p_i. + This expression will be later evaluated with k_vector. + See k_vector setter in class CableTemplate in cable_signature.sage module. - # knot_formula = "[[k[0], k[1], k[2]],\ - # [ k[3], k[4]],\ - # [-k[0], -k[3], -k[4]],\ - # [ -k[1], -k[2]]]" - # - # knot_formula = "[[k[0], k[1], k[2]],\ - # [ k[3]],\ - # [-k[0], -k[1], -k[3]],\ - # [ -k[2]]]" + Remark 1 + In the paper we used p_i and q_i to describe torus knots and cables. + It was convinient for writing, but in all the code and documentation + only 'q' letter is used to encode torus knots or cables. + Remark 2 + There are two ways to set k[i] values for a scheme: + via q_vector or via k_vector. + Both should be lists and the relation is q[i] = 2 * k[i] + 1, + i.e. q should be an odd prime and k should be an even number such that + 2 * k + 1 is prime. + To fill the scheme listed above we shoud use a list of lenght 8, + and k[0] will be ommited as it is not used in the scheme. - short_3_layers_a = "[[ k[5], k[3]], " + \ - "[ -k[1], -k[3]], " + \ - "[ k[3]], " + \ - "[ -k[4], -k[6], -k[3]]]" + Remark 3 + Except for development purposes, q_vector was computed with + a methode CableTemplate.get_q_vector and flag slice=True. + The reason for that is that we were interested only in cases + where a specific relation for each cabling-level is preserved. + Consider a cable T(2, q_0; 2, q_1; ...; 2, q_n). + Then for every q_i, q_(i + 1): q_(i + 1) > q_i * 4. - short_3_layers_b = "[[k[4], k[1], k[7]], " + \ - "[ -k[7]], " + \ - "[ k[6], k[7]], " + \ - "[ -k[5], -k[7]]]" + """ - schema_short1 = "[ [k[5], k[3]], " + \ - "[ -k[1], -k[3]], " + \ - "[ k[3]], " + \ - "[ -k[6], -k[3]]]" + # scheme that is used in the paper + lemma_scheme_a = "[ [k[5], k[3]], " + \ + "[ -k[1], -k[3]], " + \ + "[ k[3]], " + \ + "[ -k[6], -k[3]]]" - schema_short2 = "[[ k[1], k[7]], " + \ - "[ -k[7]], " + \ - "[ k[6], k[7]], " + \ - "[ -k[5], -k[7]]]" + lemma_scheme_b = "[[ k[1], k[7]], " + \ + "[ -k[7]], " + \ + "[ k[6], k[7]], " + \ + "[ -k[5], -k[7]]]" - schema_short = "[[ k[5], k[3]], " + \ + lemma_scheme = "[[ k[5], k[3]], " + \ "[ -k[1], -k[3]], " + \ "[ k[3]], " + \ "[ -k[6], -k[3]], " + \ @@ -76,40 +103,76 @@ class Schemas: "[ k[6], k[7]], " + \ "[ -k[5], -k[7]]]" - # two_summands_schema = "[ [k[0], k[1], k[4]], [-k[1], -k[3]],\ - # [k[2], k[3]], [-k[0], -k[2], -k[4]] ]" - # two_small_summands_schema = "[[k[3]], [-k[3]],\ - # [k[3]], [-k[3]] ]" # - # four_summands_schema = "[[k[3], k[2], k[0]],\ - # [ -k[2], -k[0]],\ - # [ k[1], k[0]],\ - # [-k[3], -k[1], -k[0]]]" + # formula_long = "[[k[0], k[5], k[3]], " + \ + # "[ -k[5], -k[3]], " + \ + # "[ k[2], k[3]], " + \ + # "[-k[4], -k[2], -k[3]]" + \ + # "[ k[4], k[1], k[7]], " + \ + # "[ -k[1], -k[7]], " + \ + # "[ k[6], k[7]], " + \ + # "[-k[0], -k[6], -k[7]]]" # - four_summands_schema = "[[ k[0], k[1], k[3]]," + \ - "[ -k[1], -k[3]]," + \ - "[ k[2], k[3]]," + \ - "[ -k[0], -k[2], -k[3]]]" - - # formula_1 = "[[ k[0], k[5], k[3]], " + \ + # formula_a = "[[k[0], k[5], k[3]], " + \ + # "[ -k[1], -k[3]], " + \ + # "[ k[3]], " + \ + # "[-k[4], -k[6], -k[3]]]" + # + # formula_b = "[[k[4], k[1], k[7]], " + \ + # "[ -k[7]], " + \ + # "[ k[6], k[7]], " + \ + # "[-k[0], -k[5], -k[7]]]" + # + # formula_a = "[[ k[0], k[5], k[3]], " + \ # "[ -k[1], -k[3]], " + \ # "[ k[2], k[3]], " + \ # "[ -k[0], -k[2], -k[3]]]" # - # formula_2 = "[[ k[4], k[1], k[7]], " + \ + # formula_b = "[[ k[4], k[1], k[7]], " + \ # "[ -k[5], -k[7]], " + \ # "[ k[6], k[7]], " + \ # "[ -k[4], -k[6], -k[7]]]" # - # formula_1 = "[[ k[0], k[5], k[3]], " + \ + # formula_a = "[[ k[0], k[5], k[3]], " + \ # "[ -k[5], -k[3]], " + \ # "[ k[2], k[3]], " + \ # "[-k[4], -k[2], -k[3]]]" # - # formula_2 = "[[ k[4], k[1], k[7]], " + \ + # formula_b = "[[ k[4], k[1], k[7]], " + \ # "[ -k[1], -k[7]], " + \ # "[ k[6], k[7]], " + \ # "[-k[0], -k[6], -k[7]]]" + # + # + # three_layers_formula_a = "[[k[0], k[1], k[2]],\ + # [ k[3], k[4]],\ + # [-k[0], -k[3], -k[4]],\ + # [ -k[1], -k[2]]]" + # + # three_layers_formula_b = "[[k[0], k[1], k[2]],\ + # [ k[3]],\ + # [-k[0], -k[1], -k[3]],\ + # [ -k[2]]]" + # + # short_3_layers_b = "[[ k[5], k[3]], " + \ + # "[ -k[1], -k[3]], " + \ + # "[ k[3]], " + \ + # "[ -k[4], -k[6], -k[3]]]" + # + # short_3_layers_b = "[[k[4], k[1], k[7]], " + \ + # "[ -k[7]], " + \ + # "[ k[6], k[7]], " + \ + # "[ -k[5], -k[7]]]" + # + # four_summands_scheme = "[[ k[0], k[1], k[3]]," + \ + # "[ -k[1], -k[3]]," + \ + # "[ k[2], k[3]]," + \ + # "[ -k[0], -k[2], -k[3]]]" + # + # two_summands_scheme = "[ [k[0], k[1], k[4]], [-k[1], -k[3]],\ + # [k[2], k[3]], [-k[0], -k[2], -k[4]] ]" + # two_small_summands_scheme = "[[k[3]], [-k[3]],\ + # [k[3]], [-k[3]] ]" def main(arg=None): @@ -120,43 +183,69 @@ def main(arg=None): conf = Config() cable_loop_with_details(conf) +def prove_lemma(verbose=True, details=False): -def print_sigma_for_cable(verbose=True, Schemas=None): + if verbose: + msg = "CALCULATIONS OF THE SIGMA INVARIANT\n" + msg += "Proof of main lemma from " + msg += "ON THE SLICE GENUS OF GENERALIZED ALGEBRAIC KNOTS\n\n" + print(msg) - schema_short1 = Schemas.schema_short1 - schema_short2 = Schemas.schema_short2 - schema_short = Schemas.schema_short - schema_four = Schemas.four_summands_schema + lemma_scheme = Schema.lemma_scheme - cable_template = cs.CableTemplate(knot_formula=schema_short) + cable_template = cs.CableTemplate(knot_formula=lemma_scheme, + verbose=verbose) + cable_template.fill_q_vector() + q_v = cable_template.q_vector + cable = cable_template.cable + if verbose: + msg = "Let us consider a cable knot: \nK = " + msg += cable.knot_description + ".\n" + msg += "It is an example of cable knots of a scheme:\n" + msg += str(cable_template) + "." + print(msg) + + cable.is_function_big_for_all_metabolizers(invariant=SIGMA, + verbose=verbose, + details=details) + + +def print_sigma_for_cable(verbose=True): + + lemma_scheme_a = Schema.lemma_scheme_a + lemma_scheme_b = Schema.lemma_scheme_b + lemma_scheme = Schema.lemma_scheme + scheme_four = Schema.four_summands_scheme + + cable_template = cs.CableTemplate(knot_formula=lemma_scheme) cable_template.fill_q_vector() q_v = cable_template.q_vector print(q_v) print(cable_template.cable.knot_description) - cable1 = cs.CableTemplate(knot_formula=schema_short1, + cable_a = cs.CableTemplate(knot_formula=lemma_scheme_a, verbose=verbose, q_vector=q_v ).cable - cable2 = cs.CableTemplate(knot_formula=schema_short2, + cable_b = cs.CableTemplate(knot_formula=lemma_scheme_b, verbose=verbose, q_vector=q_v ).cable - cable = cs.CableTemplate(knot_formula=schema_short1, + cable = cs.CableTemplate(knot_formula=lemma_scheme_a, verbose=verbose, q_vector=q_v ).cable cable.plot_sigma_for_summands() - # cable1.plot_sigma_for_summands() - # cable2.plot_sigma_for_summands() + # cable_a.plot_sigma_for_summands() + # cable_b.plot_sigma_for_summands() def cable_loop_with_details(verbose=True): # verbose = False - schema_short1 = Schemas.schema_short1 - schema_short2 = Schemas.schema_short2 - schema_short = Schemas.schema_short - cable_template = cs.CableTemplate(knot_formula=schema_short) + lemma_scheme_a = Schema.lemma_scheme_a + lemma_scheme_b = Schema.lemma_scheme_b + lemma_scheme = Schema.lemma_scheme + cable_template = cs.CableTemplate(knot_formula=lemma_scheme) list_of_q_vectors = [] # for el in [2, 3, 5, 7, 11, 13]: @@ -165,19 +254,23 @@ def cable_loop_with_details(verbose=True): q_v = cable_template.q_vector print(q_v) print(cable_template.cable.knot_description) - cable1 = cs.CableTemplate(knot_formula=schema_short1, + cable_a = cs.CableTemplate(knot_formula=lemma_scheme_a, verbose=verbose, q_vector=q_v ).cable - cable2 = cs.CableTemplate(knot_formula=schema_short2, + cable_b = cs.CableTemplate(knot_formula=lemma_scheme_b, verbose=verbose, q_vector=q_v ).cable # print("\n") - # print(cable1.knot_description) - is_1 = cable1.is_function_big_for_all_metabolizers(invariant=cs.SIGMA) - is_2 = cable2.is_function_big_for_all_metabolizers(invariant=cs.SIGMA) - if is_1 and is_2: + # print(cable_a.knot_description) + is_a = cable_a.is_function_big_for_all_metabolizers(invariant=cs.SIGMA, + verbose=True, + details=True) + is_b = cable_b.is_function_big_for_all_metabolizers(invariant=cs.SIGMA, + verbose=True, + details=True) + if is_a and is_b: print("sigma is big for all metabolizers") else: print("sigma is not big for all metabolizers") @@ -186,11 +279,11 @@ def cable_loop_with_details(verbose=True): def few_cable_without_calc(verbose=False): - schema_short1 = Schemas.schema_short1 - schema_short2 = Schemas.schema_short2 - schema_short = Schemas.schema_short + lemma_scheme_a = Schema.lemma_scheme_a + lemma_scheme_b = Schema.lemma_scheme_b + lemma_scheme = Schema.lemma_scheme - cable_template = cs.CableTemplate(knot_formula=schema_short) + cable_template = cs.CableTemplate(knot_formula=lemma_scheme) list_of_q_vectors = [] for el in [2, 3, 5, 7, 11, 13]: @@ -198,43 +291,23 @@ def few_cable_without_calc(verbose=False): q_v = cable_template.q_vector print(q_v) print(cable_template.cable.knot_description) - cable1 = cs.CableTemplate(knot_formula=schema_short1, + cable_a = cs.CableTemplate(knot_formula=lemma_scheme_a, verbose=verbose, q_vector=q_v ).cable - cable2 = cs.CableTemplate(knot_formula=schema_short2, + cable_b = cs.CableTemplate(knot_formula=lemma_scheme_b, verbose=verbose, q_vector=q_v ).cable - is_1 = cable1.is_function_big_for_all_metabolizers(invariant=sigma) - is_2 = cable2.is_function_big_for_all_metabolizers(invariant=sigma) - if is_1 and is_2: + is_a = cable_a.is_function_big_for_all_metabolizers(invariant=sigma) + is_b = cable_b.is_function_big_for_all_metabolizers(invariant=sigma) + if is_a and is_b: print("sigma is big for all metabolizers") else: print("sigma is not big for all metabolizers") print("\n" * 3) -def smallest_cable(verbose=True): - - schema_short1 = Schemas.schema_short1 - schema_short2 = Schemas.schema_short2 - schema_short = Schemas.schema_short - - - cable_template = cs.CableTemplate(knot_formula=schema_short) - q_v = cable_template.q_vector - print(q_v) - cable1 = cs.CableTemplate(knot_formula=schema_short1, - verbose=verbose, - q_vector=q_v).cable - cable2 = cs.CableTemplate(knot_formula=schema_short2, - verbose=verbose, - q_vector=q_v).cable - cable1.is_function_big_for_all_metabolizers(invariant=sigma) - cable2.is_function_big_for_all_metabolizers(invariant=sigma) - - def plot_many_untwisted_signature_functions(range_tuple=(1, 10)): P = Primes() for i in range(*range_tuple): @@ -250,26 +323,3 @@ if __name__ == '__main__': else: pass # main() - - -# formula_long = "[[k[0], k[5], k[3]], " + \ -# "[-k[5], -k[3]], " + \ -# "[k[2], k[3]], " + \ -# "[-k[4], -k[2], -k[3]]" + \ -# "[k[4], k[1], k[7]], " + \ -# "[-k[1], -k[7]], " + \ -# "[k[6], k[7]], " + \ -# "[-k[0], -k[6], -k[7]]]" -# -# -# formula_1 = "[[k[0], k[5], k[3]], " + \ -# "[-k[1], -k[3]], " + \ -# "[ k[3]], " + \ -# "[-k[4], -k[6], -k[3]]]" -# -# formula_2 = "[[k[4], k[1], k[7]], " + \ -# "[ -k[7]], " + \ -# "[k[6], k[7]], " + \ -# "[-k[0], -k[5], -k[7]]]" -# -# diff --git a/gaknot/signature.sage b/gaknot/signature.sage index c9fe6fd..60971c5 100644 --- a/gaknot/signature.sage +++ b/gaknot/signature.sage @@ -32,7 +32,14 @@ ipython_info = get_ipython_info() class SignatureFunction: - + r"""signature function is entirely encoded by its signature + jump, the class stores only information about signature jumps + in a dictionary self.jumps_counter + The dictionary stores data of the signature jump as a key/values pair, + where the key is the argument at which the functions jumps + and value encodes the value of the jump. Remember that we treat + signature functions as defined on the interval \[0,1). + """ def __init__(self, values=None, counter=None, plot_title=''): # counter of signature jumps @@ -367,16 +374,3 @@ class SignaturePloter: \end{document} """ f.write(tail) - - -SignatureFunction.__doc__ = \ - """ - This simple class encodes twisted and untwisted signature functions - of knots. Since the signature function is entirely encoded by its signature - jump, the class stores only information about signature jumps - in a dictionary self.jumps_counter. - The dictionary stores data of the signature jump as a key/values pair, - where the key is the argument at which the functions jumps - and value encodes the value of the jump. Remember that we treat - signature functions as defined on the interval [0,1). - """ diff --git a/gaknot/utility.py b/gaknot/utility.py index e420eb0..64bdc94 100644 --- a/gaknot/utility.py +++ b/gaknot/utility.py @@ -27,7 +27,7 @@ def import_sage(module_name, package=None, path=''): r"""Import or reload SageMath modules with preparse if the sage file exist. Arguments: - module_name - name of the module (without extension!) + module_name - name of the module (without file extension!) package - use only if module is used as a part of a package Return: module @@ -37,8 +37,6 @@ def import_sage(module_name, package=None, path=''): # equivalent to import module_name as my_prefered_shortcut} my_prefered_shortcut = import_sage('module_name') - - """ sage_name = module_name + ".sage" python_name = module_name + ".sage.py" diff --git a/notebooks/lemma.ipynb b/notebooks/lemma.ipynb new file mode 100644 index 0000000..44a0315 --- /dev/null +++ b/notebooks/lemma.ipynb @@ -0,0 +1,99 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import path\n", + "import logging\n", + "from contextlib import redirect_stdout\n", + "# logging.basicConfig(level=logging.INFO)\n", + "import gaknot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lemma " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "gaknot.prove_lemma()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Details to file" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "with open('very_detailed_calculations.txt', 'w') as f:\n", + " with redirect_stdout(f):\n", + " gaknot.prove_lemma(details=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calculations to file" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "with open('calculations.txt', 'w') as f:\n", + " with redirect_stdout(f):\n", + " gaknot.prove_lemma(details=False)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 9.0", + "language": "sage", + "name": "sagemath" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/main.ipynb b/notebooks/main.ipynb deleted file mode 100644 index 76d60a9..0000000 --- a/notebooks/main.ipynb +++ /dev/null @@ -1,268137 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Imports and settings" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "\n", - "# display full output, not only last result, except ended with semicolon\n", - "from IPython.core.interactiveshell import InteractiveShell\n", - "from IPython.display import Image, SVG\n", - "\n", - "# display full output (not only the last result)\n", - "# except lines ended with semicolon ;\n", - "InteractiveShell.ast_node_interactivity = 'all';" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "import path\n", - "import importlib\n", - "\n", - "from gaknot.utility import import_sage\n", - "# sg = import_sage('signature', package='gaknot', path=path.module_path)\n", - "# cs = import_sage('cable_signature', package='gaknot', path=path.module_path)\n", - "m = import_sage('main', package='gaknot', path=path.module_path)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Plots" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "m.plot_many_untwisted_signature_functions((6, 12))" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0, 11, 0, 83, 0, 17, 13, 103]\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83) # T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 0, 1, 1] 0\n", - "[0, 0, 2, 2] 0\n", - "[0, 0, 3, 3] 0\n", - "[0, 0, 4, 4] 4\n", - "[0, 0, 5, 5] 4\n", - "[0, 0, 6, 6] 4\n", - "[0, 0, 7, 7] 4\n", - "[0, 0, 8, 8] 4\n", - "[0, 0, 9, 9] 4\n", - "[0, 0, 10, 10] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 0, 10, 10)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 8\n", - "Sigma = 6093/83 ~ 73\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 1, 1, 0] 0\n", - "[0, 2, 2, 0] 0\n", - "[0, 3, 3, 0] 0\n", - "[0, 4, 4, 0] 4\n", - "[0, 5, 5, 0] 4\n", - "[0, 6, 6, 0] 4\n", - "[0, 7, 7, 0] 4\n", - "[0, 8, 8, 0] 4\n", - "[0, 9, 9, 0] 4\n", - "[0, 10, 10, 0] 4\n", - "[0, 11, 11, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 2, 2, 0] 0\n", - "[0, 4, 4, 0] 4\n", - "[0, 6, 6, 0] 4\n", - "[0, 8, 8, 0] 4\n", - "[0, 10, 10, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 3, 3, 0] 0\n", - "[0, 6, 6, 0] 4\n", - "[0, 9, 9, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 3, 33, 1] 115\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 3, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 4, 4, 0] 4\n", - "[0, 8, 8, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 4, 10, 1] 95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 4, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 5, 5, 0] 4\n", - "[0, 10, 10, 0] 4\n", - "[0, 15, 15, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 15, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 5, 21, 1] 107\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 5, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 6, 6, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 6, 28, 1] 111\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 6, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 7, 7, 0] 4\n", - "[0, 14, 14, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 14, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 8, 8, 0] 4\n", - "[0, 16, 16, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 16, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 8, 27, 1] 107\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 8, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 9, 9, 0] 4\n", - "[0, 18, 18, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 18, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 10, 10, 0] 4\n", - "[0, 20, 20, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 20, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 11, 11, 0] 4\n", - "[0, 22, 22, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 22, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 12, 12, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 13, 2, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 13, 2, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 13, 13, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 13, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 14, 14, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 14, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 14, 23, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 14, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 15, 15, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 15, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 16, 16, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 16, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 17, 17, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 17, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 17, 37, 1] 103\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 17, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 18, 18, 0] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 18, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 19, 14, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 19, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 19, 19, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 19, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 20, 20, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 20, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 20, 22, 1] 95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 20, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 21, 21, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 21, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 21, 39, 1] 103\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 21, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 22, 22, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 22, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 22, 30, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 22, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 23, 23, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 23, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 24, 24, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 24, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 25, 25, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 25, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 26, 26, 0] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 26, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 27, 27, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 27, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 28, 11, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 28, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 28, 28, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 28, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 29, 26, 1] 95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 29, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 29, 29, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 29, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 30, 30, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 30, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 31, 7, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 31, 7, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 31, 31, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 31, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 32, 19, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 32, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 32, 32, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 32, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 33, 29, 1] 95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 33, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 33, 33, 0] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 33, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 34, 24, 1] 95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 34, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 34, 34, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 34, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 35, 8, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 35, 8, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 35, 35, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 35, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 36, 36, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 36, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 37, 37, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 37, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 38, 38, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 38, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 39, 32, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 39, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 39, 39, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 39, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 40, 40, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 40, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 41, 41, 0] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (0, 41, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 0\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 0, 0, 1] 0\n", - "[2, 0, 0, 2] 0\n", - "[3, 0, 0, 3] -4\n", - "[4, 0, 0, 4] 0\n", - "[5, 0, 0, 5] 0\n", - "[6, 0, 0, 6] 0\n", - "[7, 0, 0, 7] 0\n", - "[8, 0, 0, 8] -4\n", - "[9, 0, 0, 9] -4\n", - "[10, 0, 0, 10] 0\n", - "[11, 0, 0, 11] 0\n", - "[12, 0, 0, 12] 0\n", - "[13, 0, 0, 13] -4\n", - "[14, 0, 0, 14] -4\n", - "[15, 0, 0, 15] -4\n", - "[16, 0, 0, 16] 0\n", - "[17, 0, 0, 17] 0\n", - "[18, 0, 0, 18] -4\n", - "[19, 0, 0, 19] -4\n", - "[20, 0, 0, 20] -4\n", - "[21, 0, 0, 21] -4\n", - "[22, 0, 0, 22] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 0, 0, 22)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 1, 0, 0] 0\n", - "[2, 2, 0, 0] 0\n", - "[3, 3, 0, 0] -4\n", - "[4, 4, 0, 0] 0\n", - "[5, 5, 0, 0] 0\n", - "[6, 6, 0, 0] 0\n", - "[7, 7, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[9, 9, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[11, 11, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[13, 13, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[15, 15, 0, 0] -4\n", - "[16, 16, 0, 0] -4\n", - "[17, 17, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 1, 1, 1] 0\n", - "[2, 2, 2, 2] 0\n", - "[3, 3, 3, 3] -4\n", - "[4, 4, 4, 4] 4\n", - "[5, 5, 5, 5] 4\n", - "[6, 6, 6, 6] 4\n", - "[7, 7, 7, 7] 4\n", - "[8, 8, 8, 8] 0\n", - "[9, 9, 9, 9] 0\n", - "[10, 10, 10, 10] 4\n", - "[11, 11, 11, 11] 4\n", - "[12, 12, 12, 12] 8\n", - "[13, 13, 13, 13] 4\n", - "[14, 14, 14, 14] 4\n", - "[15, 15, 15, 15] 4\n", - "[16, 16, 16, 16] 8\n", - "[17, 17, 17, 17] 8\n", - "[18, 18, 18, 18] 4\n", - "[19, 19, 19, 19] 8\n", - "[20, 20, 20, 20] 8\n", - "[21, 21, 21, 21] 8\n", - "[22, 22, 22, 22] 4\n", - "[23, 23, 23, 23] 8\n", - "[24, 24, 24, 24] 8\n", - "[25, 25, 25, 25] 8\n", - "[26, 26, 26, 26] 8\n", - "[27, 27, 27, 27] 8\n", - "[28, 28, 28, 28] 8\n", - "[29, 29, 29, 29] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 29, 29, 29)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 20\n", - "Sigma = 5417/83 ~ 65\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 2, 2, 1] 0\n", - "[2, 4, 4, 2] 4\n", - "[3, 6, 6, 3] 0\n", - "[4, 8, 8, 4] 4\n", - "[5, 10, 10, 5] 4\n", - "[6, 12, 12, 6] 8\n", - "[7, 14, 14, 7] 8\n", - "[8, 16, 16, 8] 4\n", - "[9, 18, 18, 9] 4\n", - "[10, 20, 20, 10] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 20, 20, 10)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 8\n", - "Sigma = 6093/83 ~ 73\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 2, 13, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 2, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 3, 3, 1] 0\n", - "[2, 6, 6, 2] 4\n", - "[3, 9, 9, 3] 0\n", - "[4, 12, 12, 4] 8\n", - "[5, 15, 15, 5] 8\n", - "[6, 18, 18, 6] 8\n", - "[7, 21, 21, 7] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 21, 21, 7)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 4, 4, 1] 4\n", - "[2, 8, 8, 2] 4\n", - "[3, 12, 12, 3] 4\n", - "[4, 16, 16, 4] 8\n", - "[5, 20, 20, 5] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 20, 20, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 5, 5, 1] 4\n", - "[2, 10, 10, 2] 4\n", - "[3, 15, 15, 3] 4\n", - "[4, 20, 20, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 20, 20, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 6, 6, 1] 4\n", - "[2, 12, 12, 2] 8\n", - "[3, 18, 18, 3] 4\n", - "[4, 24, 24, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 24, 24, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 7, 7, 1] 4\n", - "[2, 14, 14, 2] 8\n", - "[3, 21, 21, 3] 8\n", - "[4, 28, 28, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 28, 28, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 7, 31, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 7, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 8, 8, 1] 4\n", - "[2, 16, 16, 2] 8\n", - "[3, 24, 24, 3] 8\n", - "[4, 32, 32, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 32, 32, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 8, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 8, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 9, 9, 1] 4\n", - "[2, 18, 18, 2] 8\n", - "[3, 27, 27, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 27, 27, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 10, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 10, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 10, 10, 1] 4\n", - "[2, 20, 20, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 20, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 11, 11, 1] 4\n", - "[2, 22, 22, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 22, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 11, 28, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 11, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 12, 12, 1] 8\n", - "[2, 24, 24, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 24, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 13, 13, 1] 8\n", - "[2, 26, 26, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 26, 26, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 14, 14, 1] 8\n", - "[2, 28, 28, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 28, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 14, 19, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 14, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 15, 15, 1] 8\n", - "[2, 30, 30, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 30, 30, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 16, 16, 1] 8\n", - "[2, 32, 32, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 32, 32, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 17, 17, 1] 8\n", - "[2, 34, 34, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 34, 34, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 18, 18, 1] 8\n", - "[2, 36, 36, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 36, 36, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 19, 19, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 19, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 19, 32, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 19, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 20, 20, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 20, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 21, 5, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 21, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 21, 21, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 21, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 22, 20, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 22, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 22, 22, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 22, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 23, 14, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 23, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 23, 23, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 23, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 24, 24, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 24, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 24, 34, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 24, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 25, 25, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 25, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 26, 26, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 26, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 26, 29, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 26, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 27, 8, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 27, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 27, 27, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 27, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 28, 6, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 28, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 28, 28, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 28, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 29, 29, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 29, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 29, 33, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 29, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 30, 22, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 30, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 30, 30, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 30, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 31, 31, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 31, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 32, 32, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 32, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 32, 39, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 32, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 33, 3, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 33, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 33, 33, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 33, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 34, 34, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 34, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 35, 35, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 35, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 36, 36, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 36, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 37, 17, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 37, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 37, 37, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 37, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 38, 38, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 38, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 39, 21, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 39, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 39, 39, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 39, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 40, 40, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 40, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 41, 41, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (1, 41, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 1, 9, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 1, 9, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 2, 0, 0] 0\n", - "[4, 4, 0, 0] 0\n", - "[6, 6, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[14, 14, 0, 0] -4\n", - "[16, 16, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 2, 1, 1] 0\n", - "[4, 4, 2, 2] 0\n", - "[6, 6, 3, 3] 0\n", - "[8, 8, 4, 4] 0\n", - "[10, 10, 5, 5] 0\n", - "[12, 12, 6, 6] 4\n", - "[14, 14, 7, 7] 0\n", - "[16, 16, 8, 8] 0\n", - "[18, 18, 9, 9] -4\n", - "[20, 20, 10, 10] 4\n", - "[22, 22, 11, 11] 0\n", - "[24, 24, 12, 12] 0\n", - "[26, 26, 13, 13] 0\n", - "[28, 28, 14, 14] 0\n", - "[30, 30, 15, 15] 0\n", - "[32, 32, 16, 16] 0\n", - "[34, 34, 17, 17] 4\n", - "[36, 36, 18, 18] 4\n", - "[38, 38, 19, 19] 0\n", - "[40, 40, 20, 20] 0\n", - "[42, 42, 21, 21] 0\n", - "[44, 44, 22, 22] 0\n", - "[46, 46, 23, 23] 4\n", - "[48, 48, 24, 24] 8\n", - "[50, 50, 25, 25] 4\n", - "[52, 52, 26, 26] 8\n", - "[54, 54, 27, 27] 8\n", - "[56, 56, 28, 28] 8\n", - "[58, 58, 29, 29] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (58, 58, 29, 29)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 20\n", - "Sigma = 5417/83 ~ 65\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 4, 26, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 4, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 5, 41, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 5, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 6, 38, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 6, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 8, 12, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 8, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 9, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 9, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 9, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 9, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 13, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 13, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 14, 21, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 14, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 14, 39, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 14, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 16, 2, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 16, 2, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 16, 13, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 16, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 17, 6, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 17, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 17, 28, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 17, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 19, 5, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 19, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 19, 21, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 19, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 20, 8, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 20, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 20, 27, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 20, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 21, 40, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 21, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 22, 27, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 22, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 23, 32, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 23, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 23, 39, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 23, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 24, 18, 1] 8\n", - "[4, 48, 36, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 48, 36, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 25, 17, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 25, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 25, 37, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 25, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 26, 3, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 26, 3, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 27, 12, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 27, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 28, 38, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 28, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 29, 16, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 29, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 31, 25, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 31, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 32, 5, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 32, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 33, 16, 1] 4\n", - "[4, 66, 32, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 66, 32, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 35, 15, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 35, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 36, 31, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 36, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 37, 11, 1] 0\n", - "[4, 74, 22, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 74, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 37, 28, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 37, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 38, 14, 1] 4\n", - "[4, 76, 28, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 76, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 38, 19, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 38, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 39, 40, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 39, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 41, 10, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (2, 41, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 0, 18, 1] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 0, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 1, 18, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 1, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 2, 24, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 2, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 3, 0, 0] -4\n", - "[6, 6, 0, 0] 0\n", - "[9, 9, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[15, 15, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 3, 1, 1] -4\n", - "[6, 6, 2, 2] 0\n", - "[9, 9, 3, 3] -4\n", - "[12, 12, 4, 4] 4\n", - "[15, 15, 5, 5] 0\n", - "[18, 18, 6, 6] -4\n", - "[21, 21, 7, 7] 0\n", - "[24, 24, 8, 8] -4\n", - "[27, 27, 9, 9] -4\n", - "[30, 30, 10, 10] 0\n", - "[33, 33, 11, 11] -4\n", - "[36, 36, 12, 12] 0\n", - "[39, 39, 13, 13] -4\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[42, 42, 14, 14] -4\n", - "[45, 45, 15, 15] -4\n", - "[48, 48, 16, 16] 4\n", - "[51, 51, 17, 17] 0\n", - "[54, 54, 18, 18] 4\n", - "[57, 57, 19, 19] 4\n", - "[60, 60, 20, 20] 4\n", - "[63, 63, 21, 21] 8\n", - "[66, 66, 22, 22] 8\n", - "[69, 69, 23, 23] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (69, 69, 23, 23)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 69 * (83 - 69 )/83 =\n", - " = -83 + 138 * (14 )/83 =\n", - " = -83 + 138 * 14/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 69\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 69 * (83 - 69 )/83 =\n", - " = -83 + 138 * (14 )/83 =\n", - " = -83 + 138 * 14/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 16\n", - "Sigma = 5457/83 ~ 65\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 4, 16, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 4, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 5, 4, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 5, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 5, 10, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 5, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 6, 32, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 6, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 6, 39, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 6, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 7, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 7, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 7, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 7, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 10, 3, 1] -8\n", - "[6, 20, 6, 2] -4\n", - "[9, 30, 9, 3] -4\n", - "[12, 40, 12, 4] 8\n", - "[15, 50, 15, 5] 8\n", - "[18, 60, 18, 6] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 60, 18, 6)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 11, 14, 1] 8\n", - "[6, 22, 28, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 22, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 11, 19, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 11, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 13, 24, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 13, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 13, 34, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 13, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 14, 41, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 14, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 15, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 15, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 16, 9, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 16, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 17, 23, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 17, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 19, 41, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 19, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 20, 15, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 20, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 21, 10, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 21, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 22, 12, 1] 0\n", - "[6, 44, 24, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 44, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 44 * (83 - 44 )/83 =\n", - " = -83 + 88 * (39 )/83 =\n", - " = -83 + 88 * 39/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 23, 40, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 23, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 24, 22, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 24, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 24, 30, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 24, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 25, 6, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 25, 6, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 26, 2, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 26, 2, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 26, 13, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 26, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 28, 19, 1] 8\n", - "[6, 56, 38, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 56, 38, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 56 * (83 - 56 )/83 =\n", - " = -83 + 112 * (27 )/83 =\n", - " = -83 + 112 * 27/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 28, 32, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 28, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 29, 13, 1] 0\n", - "[6, 58, 26, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 58, 26, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 30, 12, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 30, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 31, 17, 1] 4\n", - "[6, 62, 34, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 62, 34, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 62 * (83 - 62 )/83 =\n", - " = -83 + 124 * (21 )/83 =\n", - " = -83 + 124 * 21/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 33, 1, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 33, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 34, 20, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 34, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 34, 22, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 34, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 37, 38, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 37, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 38, 5, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 38, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 41, 26, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (3, 41, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 0, 20, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 0, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 1, 20, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 1, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 1, 22, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 1, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 3, 34, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 3, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 4, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[16, 16, 0, 0] -4\n", - "[20, 20, 0, 0] -4\n", - "[24, 24, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 24, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 4, 1, 1] 0\n", - "[8, 8, 2, 2] -4\n", - "[12, 12, 3, 3] 0\n", - "[16, 16, 4, 4] 0\n", - "[20, 20, 5, 5] 0\n", - "[24, 24, 6, 6] -4\n", - "[28, 28, 7, 7] -4\n", - "[32, 32, 8, 8] -8\n", - "[36, 36, 9, 9] -4\n", - "[40, 40, 10, 10] -4\n", - "[44, 44, 11, 11] -4\n", - "[48, 48, 12, 12] 0\n", - "[52, 52, 13, 13] 0\n", - "[56, 56, 14, 14] 0\n", - "[60, 60, 15, 15] 0\n", - "[64, 64, 16, 16] 8\n", - "[68, 68, 17, 17] 8\n", - "[72, 72, 18, 18] 8\n", - "[76, 76, 19, 19] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (76, 76, 19, 19)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 5, 3, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 5, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 5, 33, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 5, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 6, 41, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 6, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 7, 38, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 7, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 8, 7, 1] 4\n", - "[8, 16, 14, 2] 8\n", - "[12, 24, 21, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 24, 21, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 8, 31, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 8, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 9, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 9, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 10, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 10, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 11, 40, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 11, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 13, 30, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 13, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 15, 25, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 15, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 16, 18, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 16, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 17, 5, 1] -8\n", - "[8, 34, 10, 2] 0\n", - "[12, 51, 15, 3] 8\n", - "[16, 68, 20, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 68, 20, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 18, 15, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 18, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 21, 29, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 21, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 21, 33, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 21, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 23, 4, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 23, 4, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 24, 35, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 24, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 25, 19, 1] 8\n", - "[8, 50, 38, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 50, 38, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 25, 32, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 25, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 27, 7, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 27, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 28, 41, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 28, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 29, 24, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 29, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 31, 38, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 31, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 32, 26, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 32, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 33, 24, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 33, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 33, 34, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 33, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 34, 12, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 34, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 35, 31, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 35, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 36, 6, 1] -8\n", - "[8, 72, 12, 2] 8\n", - "[12, 108, 18, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 108, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 37, 5, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 37, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 37, 21, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 37, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 38, 10, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 38, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 39, 26, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 39, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 39, 29, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 39, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 40, 16, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (4, 40, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 0, 15, 1] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 0, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 1, 15, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 1, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 2, 35, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 2, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 3, 20, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 3, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 4, 18, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 4, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 5, 0, 0] 0\n", - "[10, 10, 0, 0] -4\n", - "[15, 15, 0, 0] -4\n", - "[20, 20, 0, 0] -4\n", - "[25, 25, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 25, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 5, 1, 1] 0\n", - "[10, 10, 2, 2] -4\n", - "[15, 15, 3, 3] -4\n", - "[20, 20, 4, 4] 0\n", - "[25, 25, 5, 5] -4\n", - "[30, 30, 6, 6] -4\n", - "[35, 35, 7, 7] -4\n", - "[40, 40, 8, 8] -8\n", - "[45, 45, 9, 9] -8\n", - "[50, 50, 10, 10] -4\n", - "[55, 55, 11, 11] 0\n", - "[60, 60, 12, 12] 0\n", - "[65, 65, 13, 13] 0\n", - "[70, 70, 14, 14] 4\n", - "[75, 75, 15, 15] 4\n", - "[80, 80, 16, 16] 8\n", - "[85, 85, 17, 17] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (85, 85, 17, 17)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 85\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 85\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 12\n", - "Sigma = 5641/83 ~ 67\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 6, 26, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 6, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 6, 29, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 6, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 7, 5, 1] 4\n", - "[10, 14, 10, 2] 8\n", - "[15, 21, 15, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 21, 15, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 8, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 8, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 10, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 10, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 12, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 12, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 12, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 12, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 13, 12, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 13, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 16, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 16, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 17, 4, 1] -8\n", - "[10, 34, 8, 2] 0\n", - "[15, 51, 12, 3] 4\n", - "[20, 68, 16, 4] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 68, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 18, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 18, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 19, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 19, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 20, 25, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 20, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 21, 1, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 21, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 22, 25, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 22, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 23, 16, 1] 8\n", - "[10, 46, 32, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 46, 32, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 26, 30, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 26, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 27, 17, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 27, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 27, 37, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 27, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 28, 26, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 28, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 29, 22, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 29, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 29, 30, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 29, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 31, 40, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 31, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 32, 2, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 32, 2, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 32, 13, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 32, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 33, 20, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 33, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 33, 22, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 33, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 35, 11, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 35, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 36, 21, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 36, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 36, 39, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 36, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 37, 4, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 37, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 37, 10, 1] 0\n", - "[10, 74, 20, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 74, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 38, 3, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 38, 3, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 39, 13, 1] 4\n", - "[10, 78, 26, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 78, 26, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 40, 9, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (5, 40, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 0, 31, 1] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 0, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 1, 7, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 1, 7, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 1, 31, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 1, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 2, 36, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 2, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 4, 8, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 4, 8, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 4, 35, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 4, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 6, 0, 0] 0\n", - "[12, 12, 0, 0] 0\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 6, 1, 1] 0\n", - "[12, 12, 2, 2] 0\n", - "[18, 18, 3, 3] -8\n", - "[24, 24, 4, 4] -4\n", - "[30, 30, 5, 5] -4\n", - "[36, 36, 6, 6] -4\n", - "[42, 42, 7, 7] -8\n", - "[48, 48, 8, 8] -4\n", - "[54, 54, 9, 9] -4\n", - "[60, 60, 10, 10] 0\n", - "[66, 66, 11, 11] 4\n", - "[72, 72, 12, 12] 4\n", - "[78, 78, 13, 13] 8\n", - "[84, 84, 14, 14] 8\n", - "[90, 90, 15, 15] 8\n", - "[96, 96, 16, 16] 8\n", - "[102, 102, 17, 17] 8\n", - "[108, 108, 18, 18] 4\n", - "[114, 114, 19, 19] 4\n", - "[120, 120, 20, 20] 0\n", - "[126, 126, 21, 21] 0\n", - "[132, 132, 22, 22] 4\n", - "[138, 138, 23, 23] 8\n", - "[144, 144, 24, 24] 8\n", - "[150, 150, 25, 25] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (150, 150, 25, 25)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 150\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 67 * (83 - 67 )/83 =\n", - " = -83 + 134 * (16 )/83 =\n", - " = -83 + 134 * 16/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 150\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 67 * (83 - 67 )/83 =\n", - " = -83 + 134 * (16 )/83 =\n", - " = -83 + 134 * 16/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 16\n", - "Sigma = 5317/83 ~ 64\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 8, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 8, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 8, 32, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 8, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 10, 8, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 10, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 10, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 10, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 11, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 11, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 12, 5, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 12, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 12, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 12, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 13, 36, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 13, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 14, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 14, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 14, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 14, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 15, 40, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 15, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 17, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 17, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 18, 17, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 18, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 19, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 19, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 20, 38, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 20, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 22, 38, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 22, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 23, 24, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 23, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 25, 3, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 25, 3, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 26, 15, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 26, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 27, 14, 1] 8\n", - "[12, 54, 28, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 54, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 27, 19, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 27, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 28, 1, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 28, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 29, 15, 1] 8\n", - "[12, 58, 30, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 58, 30, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 31, 26, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 31, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 32, 18, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 32, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 34, 37, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 34, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 35, 32, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 35, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 35, 39, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 35, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 36, 4, 1] -8\n", - "[12, 72, 8, 2] 8\n", - "[18, 108, 12, 3] 4\n", - "[24, 144, 16, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 144, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 144\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 61 * (83 - 61 )/83 =\n", - " = -83 + 122 * (22 )/83 =\n", - " = -83 + 122 * 22/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 38, 9, 1] 0\n", - "[12, 76, 18, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 76, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 39, 18, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 39, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 40, 30, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 40, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 41, 20, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 41, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 41, 22, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (6, 41, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 1, 6, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 1, 6, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 2, 11, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 2, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 3, 25, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 3, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 4, 36, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 4, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 5, 15, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 5, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 6, 30, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 6, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 7, 0, 0] 0\n", - "[14, 14, 0, 0] -4\n", - "[21, 21, 0, 0] -4\n", - "[28, 28, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 28, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 7, 1, 1] 0\n", - "[14, 14, 2, 2] -4\n", - "[21, 21, 3, 3] -4\n", - "[28, 28, 4, 4] -4\n", - "[35, 35, 5, 5] -4\n", - "[42, 42, 6, 6] -8\n", - "[49, 49, 7, 7] -4\n", - "[56, 56, 8, 8] -4\n", - "[63, 63, 9, 9] 0\n", - "[70, 70, 10, 10] 4\n", - "[77, 77, 11, 11] 8\n", - "[84, 84, 12, 12] 8\n", - "[91, 91, 13, 13] 4\n", - "[98, 98, 14, 14] 4\n", - "[105, 105, 15, 15] 0\n", - "[112, 112, 16, 16] 4\n", - "[119, 119, 17, 17] 4\n", - "[126, 126, 18, 18] 0\n", - "[133, 133, 19, 19] 0\n", - "[140, 140, 20, 20] 4\n", - "[147, 147, 21, 21] 8\n", - "[154, 154, 22, 22] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (154, 154, 22, 22)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 154\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 71 * (83 - 71 )/83 =\n", - " = -83 + 142 * (12 )/83 =\n", - " = -83 + 142 * 12/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 154\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 71 * (83 - 71 )/83 =\n", - " = -83 + 142 * (12 )/83 =\n", - " = -83 + 142 * 12/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 8, 4, 1] 4\n", - "[14, 16, 8, 2] 4\n", - "[21, 24, 12, 3] 8\n", - "[28, 32, 16, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 32, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 9, 38, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 9, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 10, 36, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 10, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 12, 26, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 12, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 13, 11, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 13, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 13, 28, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 13, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 14, 8, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 14, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 14, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 14, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 15, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 15, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 15, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 15, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 16, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 16, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 17, 18, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 17, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 18, 21, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 18, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 18, 39, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 18, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 19, 8, 1] 4\n", - "[14, 38, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 38, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 19, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 19, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 21, 12, 1] 8\n", - "[14, 42, 24, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 42, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 22, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 22, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 23, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 23, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 24, 14, 1] 8\n", - "[14, 48, 28, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 48, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 24, 19, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 24, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 25, 24, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 25, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 27, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 27, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 27, 10, 1] 4\n", - "[14, 54, 20, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 54, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 30, 41, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 30, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 31, 0, 1] 67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 31, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 32, 35, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 32, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 33, 25, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 33, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 34, 19, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 34, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 34, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 34, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 36, 13, 1] 8\n", - "[14, 72, 26, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 72, 26, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 37, 18, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 37, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 38, 20, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 38, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 39, 12, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (7, 39, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 1, 41, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 1, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 2, 40, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 2, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 3, 19, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 3, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 3, 32, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 3, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 4, 6, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 4, 6, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 5, 25, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 5, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 7, 20, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 7, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 7, 22, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 7, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 8, 0, 0] -4\n", - "[16, 16, 0, 0] -4\n", - "[24, 24, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 24, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 8, 1, 1] -4\n", - "[16, 16, 2, 2] -4\n", - "[24, 24, 3, 3] -8\n", - "[32, 32, 4, 4] -8\n", - "[40, 40, 5, 5] -8\n", - "[48, 48, 6, 6] -4\n", - "[56, 56, 7, 7] -4\n", - "[64, 64, 8, 8] 0\n", - "[72, 72, 9, 9] 0\n", - "[80, 80, 10, 10] 4\n", - "[88, 88, 11, 11] 8\n", - "[96, 96, 12, 12] 4\n", - "[104, 104, 13, 13] 4\n", - "[112, 112, 14, 14] 0\n", - "[120, 120, 15, 15] -4\n", - "[128, 128, 16, 16] 0\n", - "[136, 136, 17, 17] 4\n", - "[144, 144, 18, 18] 4\n", - "[152, 152, 19, 19] 8\n", - "[160, 160, 20, 20] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (160, 160, 20, 20)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 160\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 77 * (83 - 77 )/83 =\n", - " = -83 + 154 * (6 )/83 =\n", - " = -83 + 154 * 6/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 160\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 77 * (83 - 77 )/83 =\n", - " = -83 + 154 * (6 )/83 =\n", - " = -83 + 154 * 6/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 9, 10, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 9, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 10, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 10, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 10, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 10, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 12, 9, 1] 8\n", - "[16, 24, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 24, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 13, 40, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 13, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 14, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 14, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 15, 24, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 15, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 16, 21, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 16, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 16, 39, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 16, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 17, 15, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 17, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 18, 26, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 18, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 18, 29, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 18, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 19, 7, 1] 0\n", - "[16, 38, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 38, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 19, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 19, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 20, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 20, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 23, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 23, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 25, 8, 1] -4\n", - "[16, 50, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 50, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 25, 35, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 25, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 26, 23, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 26, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 27, 1, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 27, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 29, 14, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 29, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 29, 23, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 29, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 30, 16, 1] 8\n", - "[16, 60, 32, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 60, 32, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 31, 20, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 31, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 32, 31, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 32, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 33, 14, 1] 4\n", - "[16, 66, 28, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 66, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 33, 19, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 33, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 35, 0, 1] 67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 35, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 36, 30, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 36, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 37, 12, 1] 4\n", - "[16, 74, 24, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 74, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 41, 17, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 41, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 41, 37, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (8, 41, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -6353/83 ~ -76\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 0, 13, 1] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 0, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 1, 2, 1] 8\n", - "[18, 2, 4, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 2, 4, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 1, 13, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 1, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 2, 16, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 2, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 3, 26, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 3, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 3, 29, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 3, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 5, 32, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 5, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 5, 39, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 5, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 6, 11, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 6, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 7, 36, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 7, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 9, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 9, 1, 1] -4\n", - "[18, 18, 2, 2] -8\n", - "[27, 27, 3, 3] -8\n", - "[36, 36, 4, 4] -4\n", - "[45, 45, 5, 5] -8\n", - "[54, 54, 6, 6] -4\n", - "[63, 63, 7, 7] 0\n", - "[72, 72, 8, 8] 0\n", - "[81, 81, 9, 9] 4\n", - "[90, 90, 10, 10] 8\n", - "[99, 99, 11, 11] 4\n", - "[108, 108, 12, 12] 0\n", - "[117, 117, 13, 13] 0\n", - "[126, 126, 14, 14] -4\n", - "[135, 135, 15, 15] 0\n", - "[144, 144, 16, 16] 4\n", - "[153, 153, 17, 17] 8\n", - "[162, 162, 18, 18] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (162, 162, 18, 18)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 162\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 79 * (83 - 79 )/83 =\n", - " = -83 + 158 * (4 )/83 =\n", - " = -83 + 158 * 4/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = -4\n", - "Sigma = -6589/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 162\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 79 * (83 - 79 )/83 =\n", - " = -83 + 158 * (4 )/83 =\n", - " = -83 + 158 * 4/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 12\n", - "Sigma = 5545/83 ~ 66\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 11, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 11, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 11, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 11, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 12, 8, 1] 8\n", - "[18, 24, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 24, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 12, 35, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 12, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 14, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 14, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 15, 12, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 15, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 16, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 16, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 16, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 16, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 18, 24, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 18, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 18, 34, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 18, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 19, 23, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 19, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 20, 30, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 20, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 21, 19, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 21, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 21, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 21, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 23, 38, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 23, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 24, 9, 1] 0\n", - "[18, 48, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 48, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 27, 20, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 27, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 28, 17, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 28, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 31, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 31, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 32, 14, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 32, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 32, 23, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 32, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 33, 26, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 33, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 35, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 35, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 37, 25, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 37, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 38, 6, 1] -4\n", - "[18, 76, 12, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 76, 12, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 39, 14, 1] 8\n", - "[18, 78, 28, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 78, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 39, 19, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 39, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 40, 5, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 40, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 40, 21, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 40, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 41, 40, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (9, 41, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 1, 20, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 1, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 2, 30, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 2, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 3, 18, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 3, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 4, 0, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 4, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 5, 3, 1] 8\n", - "[20, 10, 6, 2] 8\n", - "[30, 15, 9, 3] 8\n", - "[40, 20, 12, 4] 8\n", - "[50, 25, 15, 5] 8\n", - "[60, 30, 18, 6] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (60, 30, 18, 6)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 7, 38, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 7, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 8, 31, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 8, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 9, 8, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 9, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 9, 27, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 9, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 10, 0, 0] -4\n", - "[20, 20, 0, 0] -4\n", - "[30, 30, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 30, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 10, 1, 1] -4\n", - "[20, 20, 2, 2] -4\n", - "[30, 30, 3, 3] -8\n", - "[40, 40, 4, 4] -8\n", - "[50, 50, 5, 5] -8\n", - "[60, 60, 6, 6] -4\n", - "[70, 70, 7, 7] 0\n", - "[80, 80, 8, 8] 0\n", - "[90, 90, 9, 9] 4\n", - "[100, 100, 10, 10] 4\n", - "[110, 110, 11, 11] 0\n", - "[120, 120, 12, 12] -4\n", - "[130, 130, 13, 13] 0\n", - "[140, 140, 14, 14] 0\n", - "[150, 150, 15, 15] 4\n", - "[160, 160, 16, 16] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (160, 160, 16, 16)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 160\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 77 * (83 - 77 )/83 =\n", - " = -83 + 154 * (6 )/83 =\n", - " = -83 + 154 * 6/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 160\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 77 * (83 - 77 )/83 =\n", - " = -83 + 154 * (6 )/83 =\n", - " = -83 + 154 * 6/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 12\n", - "Sigma = 5741/83 ~ 69\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 11, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 11, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 12, 25, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 12, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 13, 22, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 13, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 13, 30, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 13, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 17, 40, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 17, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 18, 15, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 18, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 19, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 19, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 20, 36, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 20, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 21, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 21, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 21, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 21, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 24, 12, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 24, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 25, 32, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 25, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 25, 39, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 25, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 26, 24, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 26, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 27, 7, 1] 0\n", - "[20, 54, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 54, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 27, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 27, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 28, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 28, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 29, 24, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 29, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 29, 34, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 29, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 31, 23, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 31, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 32, 26, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 32, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 32, 29, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 32, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 33, 34, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 33, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 34, 12, 1] 8\n", - "[20, 68, 24, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 68, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 37, 5, 1] -4\n", - "[20, 74, 10, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 74, 10, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 38, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 38, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 38, 10, 1] 4\n", - "[20, 76, 20, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 76, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 39, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 39, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 39, 33, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 39, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 40, 16, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 40, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 41, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (10, 41, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 2, 7, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 2, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 4, 12, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 4, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 5, 30, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 5, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 6, 9, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 6, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 7, 26, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 7, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 7, 29, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 7, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 8, 21, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 8, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 8, 39, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 8, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 9, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 9, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 10, 35, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 10, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 11, 0, 0] -4\n", - "[22, 22, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 22, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 11, 1, 1] -4\n", - "[22, 22, 2, 2] -8\n", - "[33, 33, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 33, 3, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 12, 40, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 12, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 13, 7, 1] 8\n", - "[22, 26, 14, 2] 8\n", - "[33, 39, 21, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 39, 21, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 13, 31, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 13, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 14, 18, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 14, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 15, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 15, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 17, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 17, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 18, 11, 1] 8\n", - "[22, 36, 22, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 36, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 18, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 18, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 19, 18, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 19, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 20, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 20, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 20, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 20, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 22, 23, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 22, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 23, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 23, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 24, 17, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 24, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 24, 37, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 24, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 25, 16, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 25, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 27, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 27, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 27, 39, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 27, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 28, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 28, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 30, 38, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 30, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 31, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 31, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 31, 33, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 31, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 34, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 34, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 35, 5, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 35, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 35, 21, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 35, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 37, 2, 1] -8\n", - "[22, 74, 4, 2] 4\n", - "[33, 111, 6, 3] -4\n", - "[44, 148, 8, 4] 0\n", - "[55, 185, 10, 5] 8\n", - "[66, 222, 12, 6] 8\n", - "[77, 259, 14, 7] 8\n", - "[88, 296, 16, 8] 0\n", - "[99, 333, 18, 9] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (99, 333, 18, 9)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 99\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 333\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 37, 13, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 37, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 38, 24, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 38, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 40, 20, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 40, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 40, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (11, 40, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 0, 40, 1] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 0, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 1, 40, 0] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 1, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 2, 21, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 2, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 2, 39, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 2, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 3, 23, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 3, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 4, 11, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 4, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 5, 31, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 5, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 6, 15, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 6, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 8, 2, 1] 4\n", - "[24, 16, 4, 2] 0\n", - "[36, 24, 6, 3] -4\n", - "[48, 32, 8, 4] 0\n", - "[60, 40, 10, 5] 4\n", - "[72, 48, 12, 6] 4\n", - "[84, 56, 14, 7] -4\n", - "[96, 64, 16, 8] 8\n", - "[108, 72, 18, 9] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (108, 72, 18, 9)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4. -T(2, 13; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 8, 13, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 8, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 9, 41, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 9, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 10, 17, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 10, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 11, 12, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 11, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 12, 0, 0] 0\n", - "[24, 24, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 24, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 12, 1, 1] 0\n", - "[24, 24, 2, 2] -8\n", - "[36, 36, 3, 3] -8\n", - "[48, 48, 4, 4] -4\n", - "[60, 60, 5, 5] -4\n", - "[72, 72, 6, 6] 0\n", - "[84, 84, 7, 7] 4\n", - "[96, 96, 8, 8] 0\n", - "[108, 108, 9, 9] -4\n", - "[120, 120, 10, 10] -4\n", - "[132, 132, 11, 11] 0\n", - "[144, 144, 12, 12] 0\n", - "[156, 156, 13, 13] 4\n", - "[168, 168, 14, 14] 8\n", - "[180, 180, 15, 15] 4\n", - "[192, 192, 16, 16] 4\n", - "[204, 204, 17, 17] 0\n", - "[216, 216, 18, 18] 0\n", - "[228, 228, 19, 19] 8\n", - "[240, 240, 20, 20] 8\n", - "[252, 252, 21, 21] 8\n", - "[264, 264, 22, 22] 8\n", - "[276, 276, 23, 23] 8\n", - "[288, 288, 24, 24] 4\n", - "[300, 300, 25, 25] 4\n", - "[312, 312, 26, 26] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (312, 312, 26, 26)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 312\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 63 * (83 - 63 )/83 =\n", - " = -83 + 126 * (20 )/83 =\n", - " = -83 + 126 * 20/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 312\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 63 * (83 - 63 )/83 =\n", - " = -83 + 126 * (20 )/83 =\n", - " = -83 + 126 * 20/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 16\n", - "Sigma = 5253/83 ~ 63\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 13, 5, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 13, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 13, 21, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 13, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 15, 9, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 15, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 16, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 16, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 16, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 16, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 17, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 17, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 19, 36, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 19, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 20, 16, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 20, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 21, 7, 1] 4\n", - "[24, 42, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 42, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 21, 31, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 21, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 22, 3, 1] -4\n", - "[24, 44, 6, 2] 0\n", - "[36, 66, 9, 3] 4\n", - "[48, 88, 12, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (48, 88, 12, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 24, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 24, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 27, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 27, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 28, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 28, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 29, 38, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 29, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 30, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 30, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 30, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 30, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 31, 30, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 31, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 32, 36, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 32, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 33, 38, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 33, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 34, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 34, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 34, 10, 1] 8\n", - "[24, 68, 20, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 68, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 35, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 35, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 37, 8, 1] 4\n", - "[24, 74, 16, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 74, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 37, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 37, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 39, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 39, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 41, 25, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (12, 41, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 0, 9, 1] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 0, 9, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 1, 9, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 1, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 2, 1, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 2, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 3, 16, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 3, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 5, 40, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 5, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 6, 38, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 6, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 8, 12, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 8, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 9, 24, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 9, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 11, 6, 1] 4\n", - "[26, 22, 12, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 22, 12, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 12, 15, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 12, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 13, 0, 0] -4\n", - "[26, 26, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 26, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 13, 1, 1] -4\n", - "[26, 26, 2, 2] -8\n", - "[39, 39, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 39, 3, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 14, 32, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 14, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 14, 39, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 14, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 16, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 16, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 17, 11, 1] 8\n", - "[26, 34, 22, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 34, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 17, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 17, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 19, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 19, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 19, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 19, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 20, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 20, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 21, 40, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 21, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 23, 19, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 23, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 23, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 23, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 24, 18, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 24, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 25, 37, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 25, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 26, 3, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 26, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 26, 33, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 26, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 27, 35, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 27, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 29, 3, 1] -8\n", - "[26, 58, 6, 2] 0\n", - "[39, 87, 9, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 87, 9, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 30, 20, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 30, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 32, 5, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 32, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 32, 21, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 32, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 33, 16, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 33, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 34, 18, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 34, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 35, 12, 1] 8\n", - "[26, 70, 24, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 70, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 70 * (83 - 70 )/83 =\n", - " = -83 + 140 * (13 )/83 =\n", - " = -83 + 140 * 13/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 36, 7, 1] 0\n", - "[26, 72, 14, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 72, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 36, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 36, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 37, 11, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 37, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 38, 14, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 38, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 38, 23, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 38, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 39, 5, 1] -4\n", - "[26, 78, 10, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 78, 10, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 40, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (13, 40, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 3, 35, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 3, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 4, 22, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 4, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 4, 30, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 4, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 5, 24, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 5, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 6, 16, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 6, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 9, 36, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 9, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 10, 30, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 10, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 11, 3, 1] 0\n", - "[28, 22, 6, 2] 0\n", - "[42, 33, 9, 3] -4\n", - "[56, 44, 12, 4] 8\n", - "[70, 55, 15, 5] 8\n", - "[84, 66, 18, 6] 4\n", - "[98, 77, 21, 7] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (98, 77, 21, 7)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 77\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 77 * (83 - 77 )/83 =\n", - " = -83 + 154 * (6 )/83 =\n", - " = -83 + 154 * 6/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 12, 23, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 12, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 14, 0, 0] -4\n", - "[28, 28, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 28, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 14, 1, 1] -4\n", - "[28, 28, 2, 2] -8\n", - "[42, 42, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (42, 42, 3, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 15, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 15, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 15, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 15, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 16, 12, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 16, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 17, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 17, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 17, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 17, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 19, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 19, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 20, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 20, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 22, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 22, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 23, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 23, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 24, 7, 1] 0\n", - "[28, 48, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 48, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 24, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 24, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 26, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 26, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 27, 6, 1] 0\n", - "[28, 54, 12, 2] 8\n", - "[42, 81, 18, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (42, 81, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 81 * (83 - 81 )/83 =\n", - " = -83 + 162 * (2 )/83 =\n", - " = -83 + 162 * 2/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 28, 16, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 28, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 29, 8, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 29, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 29, 27, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 29, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 30, 17, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 30, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 30, 37, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 30, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 32, 9, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 32, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 33, 8, 1] 0\n", - "[28, 66, 16, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 66, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 33, 35, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 33, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 34, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 34, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 35, 38, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 35, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 36, 41, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 36, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[14, 37, 26, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 37, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 37, 29, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 37, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 38, 2, 1] -8\n", - "[28, 76, 4, 2] 8\n", - "[42, 114, 6, 3] -8\n", - "[56, 152, 8, 4] 8\n", - "[70, 190, 10, 5] 0\n", - "[84, 228, 12, 6] -4\n", - "[98, 266, 14, 7] 8\n", - "[112, 304, 16, 8] 8\n", - "[126, 342, 18, 9] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (126, 342, 18, 9)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 126\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 43 * (83 - 43 )/83 =\n", - " = -83 + 86 * (40 )/83 =\n", - " = -83 + 86 * 40/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 342\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 38, 13, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 38, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 39, 9, 1] 4\n", - "[28, 78, 18, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 78, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 40, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 40, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 41, 18, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (14, 41, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 0, 5, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 0, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 1, 5, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 1, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 1, 21, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 1, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 2, 19, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 2, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 2, 32, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 2, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 3, 38, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 3, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 4, 17, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 4, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 4, 37, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 4, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 5, 7, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 5, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 6, 12, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 6, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 9, 40, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 9, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 10, 37, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 10, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 11, 35, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 11, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 12, 13, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 12, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 13, 32, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 13, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 13, 39, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 13, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 15, 0, 0] -4\n", - "[30, 30, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 30, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 15, 1, 1] -4\n", - "[30, 30, 2, 2] -8\n", - "[45, 45, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (45, 45, 3, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 45 * (83 - 45 )/83 =\n", - " = -83 + 90 * (38 )/83 =\n", - " = -83 + 90 * 38/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 45 * (83 - 45 )/83 =\n", - " = -83 + 90 * (38 )/83 =\n", - " = -83 + 90 * 38/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 16, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 16, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 17, 8, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 17, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 17, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 17, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 18, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 18, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 18, 10, 1] 8\n", - "[30, 36, 20, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 36, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 20, 3, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 20, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 20, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 20, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 21, 36, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 21, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 22, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 22, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 22, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 22, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 25, 20, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 25, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 25, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 25, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 26, 6, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 26, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 26, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 26, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 27, 16, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 27, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 28, 12, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 28, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 29, 6, 1] 0\n", - "[30, 58, 12, 2] 8\n", - "[45, 87, 18, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (45, 87, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 45 * (83 - 45 )/83 =\n", - " = -83 + 90 * (38 )/83 =\n", - " = -83 + 90 * 38/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 30, 26, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 30, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 30, 29, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 30, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 35, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 35, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 36, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 36, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 37, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 37, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 39, 36, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 39, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 40, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (15, 40, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 0, 34, 1] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 0, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 1, 24, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 1, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 1, 34, 0] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 1, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 2, 9, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 2, 9, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 3, 13, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 3, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 4, 3, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 4, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 4, 33, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 4, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 6, 14, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 6, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 6, 19, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 6, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 9, 18, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 9, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 10, 29, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 10, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 10, 33, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 10, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 11, 23, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 11, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 14, 40, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 14, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 16, 0, 0] -4\n", - "[32, 32, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 32, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 16, 1, 1] -4\n", - "[32, 32, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 32, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 17, 38, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 17, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 18, 20, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 18, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 18, 22, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 18, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 19, 40, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 19, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 20, 12, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 20, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 22, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 22, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 23, 5, 1] 0\n", - "[32, 46, 10, 2] 4\n", - "[48, 69, 15, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (48, 69, 15, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 69\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 69 * (83 - 69 )/83 =\n", - " = -83 + 138 * (14 )/83 =\n", - " = -83 + 138 * 14/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 25, 11, 1] 8\n", - "[32, 50, 22, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 50, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 25, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 25, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 27, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 27, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 28, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 28, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 28, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 28, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 29, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 29, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 30, 8, 1] 4\n", - "[32, 60, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 60, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 30, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 30, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 31, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 31, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 32, 41, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 32, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 33, 2, 1] -8\n", - "[32, 66, 4, 2] -4\n", - "[48, 99, 6, 3] 0\n", - "[64, 132, 8, 4] 4\n", - "[80, 165, 10, 5] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (80, 165, 10, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 165\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 33, 13, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 33, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 34, 30, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 34, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 36, 25, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 36, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 38, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 38, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 38, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 38, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 39, 41, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 39, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 40, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (16, 40, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = -12\n", - "Sigma = -5741/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 40, 10, 1] 8\n", - "[32, 80, 20, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 80, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 0, 25, 1] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 0, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 1, 25, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 1, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 2, 31, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 2, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 4, 15, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 4, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 5, 20, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 5, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 5, 22, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 5, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 7, 3, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 7, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 7, 33, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 7, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 8, 5, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 8, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 9, 37, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 9, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 10, 12, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 10, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 11, 9, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 11, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 12, 41, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 12, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 16, 36, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 16, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 17, 0, 0] -4\n", - "[34, 34, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 34, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 17, 1, 1] -4\n", - "[34, 34, 2, 2] -8\n", - "[51, 51, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (51, 51, 3, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 51 * (83 - 51 )/83 =\n", - " = -83 + 102 * (32 )/83 =\n", - " = -83 + 102 * 32/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 51 * (83 - 51 )/83 =\n", - " = -83 + 102 * (32 )/83 =\n", - " = -83 + 102 * 32/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 18, 6, 1] 4\n", - "[34, 36, 12, 2] 8\n", - "[51, 54, 18, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (51, 54, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 51 * (83 - 51 )/83 =\n", - " = -83 + 102 * (32 )/83 =\n", - " = -83 + 102 * 32/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 20, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 20, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 20, 32, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 20, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 21, 22, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 21, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 21, 30, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 21, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 22, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 22, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 22, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 22, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 23, 18, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 23, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 24, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 24, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 25, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 25, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 27, 5, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 27, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 27, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 27, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 28, 9, 1] 8\n", - "[34, 56, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 56, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 56 * (83 - 56 )/83 =\n", - " = -83 + 112 * (27 )/83 =\n", - " = -83 + 112 * 27/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 30, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 30, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 30, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 30, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 31, 3, 1] -4\n", - "[34, 62, 6, 2] 0\n", - "[51, 93, 9, 3] 8\n", - "[68, 124, 12, 4] 8\n", - "[85, 155, 15, 5] 8\n", - "[102, 186, 18, 6] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (102, 186, 18, 6)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 186\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 34, 11, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 34, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 34, 28, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 34, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 35, 40, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 35, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 36, 26, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 36, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 36, 29, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 36, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 37, 1, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 37, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 38, 34, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 38, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 39, 30, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 39, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 41, 8, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 41, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 41, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (17, 41, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 0, 3, 1] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 0, 3, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 1, 3, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 1, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 1, 33, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 1, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 2, 26, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 2, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 3, 10, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 3, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 4, 5, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 4, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 5, 38, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 5, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 6, 25, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 6, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 9, 16, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 9, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 10, 5, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 10, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 10, 21, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 10, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 12, 22, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 12, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 12, 30, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 12, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 13, 26, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 13, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 13, 29, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 13, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 14, 11, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 14, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 15, 20, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 15, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 16, 4, 1] 0\n", - "[36, 32, 8, 2] 0\n", - "[54, 48, 12, 3] 8\n", - "[72, 64, 16, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (72, 64, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 17, 7, 1] 4\n", - "[36, 34, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 34, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 17, 31, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 17, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 18, 1, 1] -8\n", - "[36, 36, 2, 2] -8\n", - "[54, 54, 3, 3] -8\n", - "[72, 72, 4, 4] 0\n", - "[90, 90, 5, 5] 4\n", - "[108, 108, 6, 6] -4\n", - "[126, 126, 7, 7] -8\n", - "[144, 144, 8, 8] -4\n", - "[162, 162, 9, 9] 4\n", - "[180, 180, 10, 10] 4\n", - "[198, 198, 11, 11] -4\n", - "[216, 216, 12, 12] -4\n", - "[234, 234, 13, 13] 4\n", - "[252, 252, 14, 14] 4\n", - "[270, 270, 15, 15] 4\n", - "[288, 288, 16, 16] 0\n", - "[306, 306, 17, 17] 4\n", - "[324, 324, 18, 18] 8\n", - "[342, 342, 19, 19] 8\n", - "[360, 360, 20, 20] 4\n", - "[378, 378, 21, 21] 0\n", - "[396, 396, 22, 22] 8\n", - "[414, 414, 23, 23] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (414, 414, 23, 23)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 414\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 414\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 16\n", - "Sigma = 5457/83 ~ 65\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 19, 11, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 19, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 19, 28, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 19, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 20, 34, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 20, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 22, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 22, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 22, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 22, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 23, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 23, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 24, 2, 1] -8\n", - "[36, 48, 4, 2] -4\n", - "[54, 72, 6, 3] 4\n", - "[72, 96, 8, 4] 8\n", - "[90, 120, 10, 5] 0\n", - "[108, 144, 12, 6] 8\n", - "[126, 168, 14, 7] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (126, 168, 14, 7)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 126\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 43 * (83 - 43 )/83 =\n", - " = -83 + 86 * (40 )/83 =\n", - " = -83 + 86 * 40/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 168\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 24, 13, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 24, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 26, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 26, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 30, 24, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 30, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 32, 6, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 32, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 32, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 32, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 34, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 34, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 36, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 36, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 37, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 37, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 38, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 38, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 39, 6, 1] 0\n", - "[36, 78, 12, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 78, 12, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 40, 23, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 40, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 41, 14, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 41, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 41, 19, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (18, 41, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -5877/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 2, 15, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 2, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 3, 8, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 3, 8, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 3, 35, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 3, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 4, 30, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 4, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 6, 16, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 6, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 7, 41, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 7, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 8, 6, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 8, 6, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 11, 3, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 11, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 11, 33, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 11, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 12, 38, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 12, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 14, 1, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 14, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 15, 14, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 15, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 15, 23, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 15, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 16, 12, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 16, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 17, 26, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 17, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 17, 29, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 17, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 19, 0, 0] -4\n", - "[38, 38, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 38, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 19, 1, 1] -4\n", - "[38, 38, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 38, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 20, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 20, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 21, 9, 1] 8\n", - "[38, 42, 18, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 42, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 22, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 22, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 22, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 22, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 23, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 23, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 24, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 24, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 25, 4, 1] -4\n", - "[38, 50, 8, 2] -4\n", - "[57, 75, 12, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (57, 75, 12, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 57 * (83 - 57 )/83 =\n", - " = -83 + 114 * (26 )/83 =\n", - " = -83 + 114 * 26/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 75 * (83 - 75 )/83 =\n", - " = -83 + 150 * (8 )/83 =\n", - " = -83 + 150 * 8/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 27, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 27, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 27, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 27, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 28, 3, 1] -4\n", - "[38, 56, 6, 2] -4\n", - "[57, 84, 9, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (57, 84, 9, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 57 * (83 - 57 )/83 =\n", - " = -83 + 114 * (26 )/83 =\n", - " = -83 + 114 * 26/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 29, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 29, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 30, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 30, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 32, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 32, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 33, 8, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 33, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 33, 27, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 33, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 34, 7, 1] 4\n", - "[38, 68, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 68, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 34, 31, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 34, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 36, 40, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 36, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 37, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 37, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 38, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 38, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 39, 9, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 39, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 40, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 40, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 40, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 40, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 41, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (19, 41, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 0, 4, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 0, 4, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 1, 4, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 1, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 1, 10, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 1, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 3, 5, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 3, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 4, 23, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 4, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 5, 17, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 5, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 5, 37, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 5, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 6, 36, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 6, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 7, 8, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 7, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 7, 27, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 7, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 10, 38, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 10, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 12, 34, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 12, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 15, 18, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 15, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 16, 40, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 16, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 18, 16, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 18, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 19, 25, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 19, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 20, 0, 0] -4\n", - "[40, 40, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 40, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 20, 1, 1] -4\n", - "[40, 40, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 40, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 21, 37, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 21, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 22, 1, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 22, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 24, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 24, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 24, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 24, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 25, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 25, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 26, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 26, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 26, 39, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 26, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 27, 9, 1] 8\n", - "[40, 54, 18, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 54, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[20, 29, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 29, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 29, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 29, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 30, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 30, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 31, 8, 1] 4\n", - "[40, 62, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 62, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 62 * (83 - 62 )/83 =\n", - " = -83 + 124 * (21 )/83 =\n", - " = -83 + 124 * 21/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 31, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 31, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 32, 25, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 32, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 33, 5, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 33, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 33, 21, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 33, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 34, 3, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 34, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 34, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 34, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 35, 24, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 35, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 38, 7, 1] 4\n", - "[40, 76, 14, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 76, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 38, 31, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 38, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 40, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 40, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 41, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 41, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 41, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (20, 41, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = -16\n", - "Sigma = -5697/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 1, 15, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 1, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 2, 12, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 2, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 5, 0, 1] 91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 5, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 6, 29, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 6, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 6, 33, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 6, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 7, 40, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 7, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 8, 11, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 8, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 10, 18, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 10, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 11, 26, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 11, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 12, 6, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 12, 6, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 13, 12, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 13, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 14, 2, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 14, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 15, 38, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 15, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 16, 8, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 16, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 16, 27, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 16, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 18, 7, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 18, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 19, 2, 1] 0\n", - "[42, 38, 4, 2] -8\n", - "[63, 57, 6, 3] -4\n", - "[84, 76, 8, 4] 4\n", - "[105, 95, 10, 5] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (105, 95, 10, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 95\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 19, 13, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 19, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 21, 0, 0] -4\n", - "[42, 42, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (42, 42, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 21, 1, 1] -4\n", - "[42, 42, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (42, 42, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 22, 25, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 22, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 26, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 26, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 26, 30, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 26, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 27, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 27, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 28, 26, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 28, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 28, 29, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 28, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 29, 20, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 29, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 29, 22, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 29, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 30, 25, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 30, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 31, 40, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 31, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 32, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 32, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 33, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 33, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 34, 36, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 34, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 35, 11, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 35, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 35, 28, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 35, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 36, 5, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 36, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 36, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 36, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 37, 4, 1] 0\n", - "[42, 74, 8, 2] 8\n", - "[63, 111, 12, 3] 8\n", - "[84, 148, 16, 4] 4\n", - "[105, 185, 20, 5] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (105, 185, 20, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 185\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 38, 16, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 38, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 39, 1, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 39, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 40, 9, 1] 8\n", - "[42, 80, 18, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (42, 80, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 41, 24, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (21, 41, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 1, 4, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 1, 4, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 3, 40, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 3, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 4, 14, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 4, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 4, 23, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 4, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 5, 17, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 5, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 6, 36, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 6, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 7, 8, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 7, 8, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 7, 35, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 7, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 8, 24, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 8, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 9, 26, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 9, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 10, 23, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 10, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 12, 18, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 12, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 13, 10, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 13, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 14, 25, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 14, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 16, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 16, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 18, 16, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 18, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 19, 25, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 19, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 20, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 20, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 21, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 21, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 21, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 21, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 22, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 22, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 22, 1, 1] -8\n", - "[44, 44, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (44, 44, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 44 * (83 - 44 )/83 =\n", - " = -83 + 88 * (39 )/83 =\n", - " = -83 + 88 * 39/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 44 * (83 - 44 )/83 =\n", - " = -83 + 88 * (39 )/83 =\n", - " = -83 + 88 * 39/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 24, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 24, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 24, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 24, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 25, 15, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 25, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 26, 21, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 26, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 26, 39, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 26, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 28, 36, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 28, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 29, 5, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 29, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 29, 21, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 29, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 30, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 30, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 31, 35, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 31, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 33, 5, 1] -4\n", - "[44, 66, 10, 2] 4\n", - "[66, 99, 15, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (66, 99, 15, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 34, 3, 1] -4\n", - "[44, 68, 6, 2] 0\n", - "[66, 102, 9, 3] 8\n", - "[88, 136, 12, 4] 0\n", - "[110, 170, 15, 5] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (110, 170, 15, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 110\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 170\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 35, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 35, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 35, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 35, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 36, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 36, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 38, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 38, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 39, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 39, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 40, 11, 1] 8\n", - "[44, 80, 22, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (44, 80, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 44 * (83 - 44 )/83 =\n", - " = -83 + 88 * (39 )/83 =\n", - " = -83 + 88 * 39/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 40, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (22, 40, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 41, 6, 1] 0\n", - "[44, 82, 12, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (44, 82, 12, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 44 * (83 - 44 )/83 =\n", - " = -83 + 88 * (39 )/83 =\n", - " = -83 + 88 * 39/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 3, 12, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 3, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 4, 20, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 4, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 4, 22, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 4, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 5, 24, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 5, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 5, 34, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 5, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 8, 38, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 8, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 9, 36, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 9, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 10, 22, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 10, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 10, 30, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 10, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 11, 16, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 11, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 12, 14, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 12, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 12, 23, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 12, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 14, 0, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 14, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 15, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 15, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 15, 32, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 15, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 16, 15, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 16, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 17, 3, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 17, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 17, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 17, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 18, 25, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 18, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 19, 9, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 19, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 20, 11, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 20, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 20, 28, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 20, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 21, 24, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 21, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 22, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 22, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 23, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 23, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 23, 1, 1] -8\n", - "[46, 46, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (46, 46, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 24, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 24, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 26, 8, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 26, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 26, 27, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 26, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 28, 16, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 28, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 29, 8, 1] 4\n", - "[46, 58, 16, 2] 8\n", - "[69, 87, 24, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (69, 87, 24, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 69 * (83 - 69 )/83 =\n", - " = -83 + 138 * (14 )/83 =\n", - " = -83 + 138 * 14/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 29, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 29, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 30, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 30, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 31, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 31, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 32, 9, 1] 4\n", - "[46, 64, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (46, 64, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 33, 35, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 33, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 35, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 35, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 36, 41, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 36, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 37, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 37, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 37, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 37, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 38, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 38, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 40, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (23, 40, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = -20\n", - "Sigma = -5789/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 1, 16, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 1, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 2, 3, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 2, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 2, 33, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 2, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 4, 41, 0] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 4, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 5, 14, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 5, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 5, 23, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 5, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 6, 37, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 6, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 8, 22, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 8, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 8, 30, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 8, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 9, 2, 1] 4\n", - "[48, 18, 4, 2] -4\n", - "[72, 27, 6, 3] -4\n", - "[96, 36, 8, 4] 0\n", - "[120, 45, 10, 5] 0\n", - "[144, 54, 12, 6] 4\n", - "[168, 63, 14, 7] 0\n", - "[192, 72, 16, 8] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (192, 72, 16, 8)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 192\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 9, 13, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 9, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 10, 40, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 10, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 11, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 11, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 13, 3, 1] 4\n", - "[48, 26, 6, 2] -4\n", - "[72, 39, 9, 3] 0\n", - "[96, 52, 12, 4] 4\n", - "[120, 65, 15, 5] 8\n", - "[144, 78, 18, 6] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (144, 78, 18, 6)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 61 * (83 - 61 )/83 =\n", - " = -83 + 122 * (22 )/83 =\n", - " = -83 + 122 * 22/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 14, 6, 1] 8\n", - "[48, 28, 12, 2] 8\n", - "[72, 42, 18, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (72, 42, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 15, 8, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 15, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 15, 27, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 15, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 16, 26, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 16, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 18, 9, 1] 8\n", - "[48, 36, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (48, 36, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 21, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 21, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 22, 18, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 22, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 23, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 23, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 23, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 23, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 24, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 24, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 24, 1, 1] -8\n", - "[48, 48, 2, 2] -8\n", - "[72, 72, 3, 3] -4\n", - "[96, 96, 4, 4] 0\n", - "[120, 120, 5, 5] -8\n", - "[144, 144, 6, 6] -4\n", - "[168, 168, 7, 7] 4\n", - "[192, 192, 8, 8] -4\n", - "[216, 216, 9, 9] -8\n", - "[240, 240, 10, 10] 4\n", - "[264, 264, 11, 11] 4\n", - "[288, 288, 12, 12] -4\n", - "[312, 312, 13, 13] 4\n", - "[336, 336, 14, 14] 8\n", - "[360, 360, 15, 15] 0\n", - "[384, 384, 16, 16] 4\n", - "[408, 408, 17, 17] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (408, 408, 17, 17)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 408\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 408\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 12\n", - "Sigma = 5641/83 ~ 67\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 25, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 25, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 26, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 26, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 27, 30, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 27, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 29, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 29, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 29, 10, 1] 8\n", - "[48, 58, 20, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (48, 58, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 30, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 30, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 32, 38, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 32, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 33, 4, 1] -4\n", - "[48, 66, 8, 2] 4\n", - "[72, 99, 12, 3] 8\n", - "[96, 132, 16, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (96, 132, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 132\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 49 * (83 - 49 )/83 =\n", - " = -83 + 98 * (34 )/83 =\n", - " = -83 + 98 * 34/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 34, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 34, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 35, 20, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 35, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 35, 22, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 35, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 38, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 38, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 39, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 39, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 40, 19, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 40, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 40, 32, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 40, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 41, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 41, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 41, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (24, 41, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 0, 17, 1] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 0, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 1, 17, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 1, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 1, 37, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 1, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 2, 25, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 2, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 3, 7, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 3, 7, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 3, 31, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 3, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 5, 8, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 5, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 5, 27, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 5, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 6, 18, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 6, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 8, 41, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 8, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 9, 11, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 9, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 9, 28, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 9, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 11, 24, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 11, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 11, 34, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 11, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 12, 10, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 12, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 14, 22, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 14, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 14, 30, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 14, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 15, 4, 1] 4\n", - "[50, 30, 8, 2] 0\n", - "[75, 45, 12, 3] 0\n", - "[100, 60, 16, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (100, 60, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 18, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 18, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 19, 20, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 19, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 19, 22, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 19, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 20, 5, 1] 4\n", - "[50, 40, 10, 2] 4\n", - "[75, 60, 15, 3] 4\n", - "[100, 80, 20, 4] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (100, 80, 20, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 21, 27, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 21, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 22, 5, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 22, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 22, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 22, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 23, 30, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 23, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 25, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 25, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 25, 1, 1] -8\n", - "[50, 50, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (50, 50, 2, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 26, 36, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 26, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 27, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 27, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 28, 34, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 28, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 29, 36, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 29, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 30, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 30, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 30, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 30, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 31, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 31, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 32, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 32, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 33, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 33, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 34, 38, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 34, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 36, 16, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 36, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 37, 9, 1] 8\n", - "[50, 74, 18, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (50, 74, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 40, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 40, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 41, 12, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (25, 41, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 2, 18, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 2, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 3, 9, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 3, 9, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 4, 2, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 4, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 6, 5, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 6, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 7, 11, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 7, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 7, 28, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 7, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 9, 22, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 9, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 9, 30, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 9, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 11, 21, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 11, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 11, 39, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 11, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 12, 7, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 12, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 13, 18, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 13, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 15, 31, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 15, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 16, 24, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 16, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 17, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 17, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 17, 32, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 17, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 18, 8, 1] 8\n", - "[52, 36, 16, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (52, 36, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 52 * (83 - 52 )/83 =\n", - " = -83 + 104 * (31 )/83 =\n", - " = -83 + 104 * 31/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 18, 35, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 18, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 19, 10, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 19, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 25, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 25, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 26, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 26, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 26, 1, 1] -8\n", - "[52, 52, 2, 2] -8\n", - "[78, 78, 3, 3] 0\n", - "[104, 104, 4, 4] 0\n", - "[130, 130, 5, 5] -4\n", - "[156, 156, 6, 6] 0\n", - "[182, 182, 7, 7] 0\n", - "[208, 208, 8, 8] -8\n", - "[234, 234, 9, 9] 0\n", - "[260, 260, 10, 10] 4\n", - "[286, 286, 11, 11] -4\n", - "[312, 312, 12, 12] 4\n", - "[338, 338, 13, 13] 8\n", - "[364, 364, 14, 14] -4\n", - "[390, 390, 15, 15] 0\n", - "[416, 416, 16, 16] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (416, 416, 16, 16)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 416\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 416\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 12\n", - "Sigma = 5741/83 ~ 69\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 28, 5, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 28, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 28, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 28, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 29, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 29, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 30, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 30, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 31, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 31, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 31, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 31, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 32, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 32, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 32, 10, 1] 8\n", - "[52, 64, 20, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (52, 64, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 52 * (83 - 52 )/83 =\n", - " = -83 + 104 * (31 )/83 =\n", - " = -83 + 104 * 31/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 33, 9, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 33, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 34, 27, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 34, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 35, 36, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 35, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 36, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 36, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 37, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 37, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 37, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 37, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 38, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 38, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 39, 4, 1] 0\n", - "[52, 78, 8, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (52, 78, 8, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 52 * (83 - 52 )/83 =\n", - " = -83 + 104 * (31 )/83 =\n", - " = -83 + 104 * 31/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 40, 26, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 40, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 40, 29, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 40, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 41, 3, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 41, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 41, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (26, 41, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 2, 40, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 2, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 3, 32, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 3, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 3, 39, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 3, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 5, 25, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 5, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 7, 20, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 7, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 8, 0, 1] 83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 8, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 9, 4, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 9, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 9, 10, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 9, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 10, 6, 1] 8\n", - "[54, 20, 12, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (54, 20, 12, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 13, 41, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 13, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 14, 7, 1] 8\n", - "[54, 28, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (54, 28, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 14, 31, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 14, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 15, 24, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 15, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 15, 34, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 15, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 16, 5, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 16, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 16, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 16, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 17, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 17, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 18, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 18, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 18, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 18, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 19, 31, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 19, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 20, 2, 1] -4\n", - "[54, 40, 4, 2] -4\n", - "[81, 60, 6, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (81, 60, 6, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 81 * (83 - 81 )/83 =\n", - " = -83 + 162 * (2 )/83 =\n", - " = -83 + 162 * 2/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 20, 13, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 20, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 21, 25, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 21, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 22, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 22, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 23, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 23, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 25, 35, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 25, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 26, 14, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 26, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 26, 23, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 26, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 27, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 27, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 27, 1, 1] -8\n", - "[54, 54, 2, 2] -8\n", - "[81, 81, 3, 3] 0\n", - "[108, 108, 4, 4] -4\n", - "[135, 135, 5, 5] -4\n", - "[162, 162, 6, 6] 4\n", - "[189, 189, 7, 7] -4\n", - "[216, 216, 8, 8] -8\n", - "[243, 243, 9, 9] 4\n", - "[270, 270, 10, 10] 4\n", - "[297, 297, 11, 11] 0\n", - "[324, 324, 12, 12] 4\n", - "[351, 351, 13, 13] 4\n", - "[378, 378, 14, 14] -4\n", - "[405, 405, 15, 15] 4\n", - "[432, 432, 16, 16] 8\n", - "[459, 459, 17, 17] 0\n", - "[486, 486, 18, 18] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (486, 486, 18, 18)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 486\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 71 * (83 - 71 )/83 =\n", - " = -83 + 142 * (12 )/83 =\n", - " = -83 + 142 * 12/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 486\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 71 * (83 - 71 )/83 =\n", - " = -83 + 142 * (12 )/83 =\n", - " = -83 + 142 * 12/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 12\n", - "Sigma = 5545/83 ~ 66\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 29, 14, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 29, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 29, 19, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 29, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 33, 19, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 33, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 33, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 33, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 34, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 34, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 35, 9, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 35, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 36, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 36, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 36, 30, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 36, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 37, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 37, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 38, 36, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 38, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 40, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 40, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 41, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (27, 41, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = -24\n", - "Sigma = -5857/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 1, 31, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 1, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 2, 36, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 2, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 4, 35, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 4, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 6, 0, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 6, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 7, 26, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 7, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 8, 32, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 8, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 8, 39, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 8, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 9, 25, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 9, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 10, 8, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 10, 8, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 10, 35, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 10, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 11, 1, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 11, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 12, 5, 1] 8\n", - "[56, 24, 10, 2] 4\n", - "[84, 36, 15, 3] 0\n", - "[112, 48, 20, 4] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (112, 48, 20, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 112\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 13, 7, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 13, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 14, 34, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 14, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 15, 40, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 15, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 17, 2, 1] -4\n", - "[56, 34, 4, 2] -4\n", - "[84, 51, 6, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (84, 51, 6, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 51 * (83 - 51 )/83 =\n", - " = -83 + 102 * (32 )/83 =\n", - " = -83 + 102 * 32/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 17, 13, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 17, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 18, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 18, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 19, 18, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 19, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 20, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 20, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 22, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 22, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 23, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 23, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 23, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 23, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 24, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 24, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 25, 16, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 25, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 26, 15, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 26, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 27, 19, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 27, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 27, 32, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 27, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 28, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 28, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 28, 1, 1] -8\n", - "[56, 56, 2, 2] -8\n", - "[84, 84, 3, 3] 0\n", - "[112, 112, 4, 4] -4\n", - "[140, 140, 5, 5] -4\n", - "[168, 168, 6, 6] 4\n", - "[196, 196, 7, 7] -4\n", - "[224, 224, 8, 8] -4\n", - "[252, 252, 9, 9] 0\n", - "[280, 280, 10, 10] 0\n", - "[308, 308, 11, 11] 0\n", - "[336, 336, 12, 12] 8\n", - "[364, 364, 13, 13] -4\n", - "[392, 392, 14, 14] 0\n", - "[420, 420, 15, 15] 8\n", - "[448, 448, 16, 16] 0\n", - "[476, 476, 17, 17] 4\n", - "[504, 504, 18, 18] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (504, 504, 18, 18)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 504\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = -4\n", - "Sigma = -6297/83 ~ -75\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 504\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 12\n", - "Sigma = 5545/83 ~ 66\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 30, 38, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 30, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 31, 26, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 31, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 31, 29, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 31, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 32, 18, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 32, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 34, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 34, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 34, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 34, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 35, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 35, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 35, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 35, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 37, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 37, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 40, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 40, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 40, 30, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 40, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 41, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (28, 41, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 2, 34, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 2, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 3, 9, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 3, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 6, 5, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 6, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 6, 21, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 6, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 7, 11, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 7, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 9, 30, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 9, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 10, 16, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 10, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 11, 32, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 11, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 11, 39, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 11, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 12, 36, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 12, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 13, 18, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 13, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 15, 7, 1] 8\n", - "[58, 30, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (58, 30, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 15, 31, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 15, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 17, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 17, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 17, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 17, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 18, 8, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 18, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 18, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 18, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 21, 4, 1] 0\n", - "[58, 42, 8, 2] 4\n", - "[87, 63, 12, 3] 0\n", - "[116, 84, 16, 4] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (116, 84, 16, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 116\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 22, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 22, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 23, 41, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 23, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 24, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 24, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 25, 38, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 25, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 26, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 26, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 28, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 28, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 28, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 28, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 29, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 29, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 29, 1, 1] -8\n", - "[58, 58, 2, 2] -8\n", - "[87, 87, 3, 3] 0\n", - "[116, 116, 4, 4] -8\n", - "[145, 145, 5, 5] 0\n", - "[174, 174, 6, 6] 0\n", - "[203, 203, 7, 7] -8\n", - "[232, 232, 8, 8] 0\n", - "[261, 261, 9, 9] 4\n", - "[290, 290, 10, 10] -4\n", - "[319, 319, 11, 11] 4\n", - "[348, 348, 12, 12] 4\n", - "[377, 377, 13, 13] -4\n", - "[406, 406, 14, 14] 4\n", - "[435, 435, 15, 15] 4\n", - "[464, 464, 16, 16] 4\n", - "[493, 493, 17, 17] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (493, 493, 17, 17)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 493\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 493\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 12\n", - "Sigma = 5641/83 ~ 67\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 30, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 30, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 31, 11, 1] 8\n", - "[58, 62, 22, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (58, 62, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 62 * (83 - 62 )/83 =\n", - " = -83 + 124 * (21 )/83 =\n", - " = -83 + 124 * 21/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 31, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 31, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 32, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 32, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 33, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 33, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 36, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 36, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 36, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 36, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 37, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 37, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 37, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 37, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 38, 40, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 38, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 39, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 39, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 39, 10, 1] 8\n", - "[58, 78, 20, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (58, 78, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 40, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 40, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 41, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 41, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 41, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (29, 41, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5749/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 2, 10, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 2, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 3, 40, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 3, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 4, 14, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 4, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 4, 19, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 4, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 5, 11, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 5, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 6, 7, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 6, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 7, 35, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 7, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 8, 24, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 8, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 8, 34, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 8, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 9, 26, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 9, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 9, 29, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 9, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 10, 14, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 10, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 10, 23, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 10, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 11, 36, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 11, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 12, 18, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 12, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 13, 4, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 13, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 13, 10, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 13, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 14, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 14, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 16, 41, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 16, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 20, 9, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 20, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 21, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 21, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 22, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 22, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 23, 25, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 23, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 24, 3, 1] -4\n", - "[60, 48, 6, 2] 0\n", - "[90, 72, 9, 3] 4\n", - "[120, 96, 12, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (120, 96, 12, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 26, 5, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 26, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 26, 21, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 26, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 27, 24, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 27, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 28, 36, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 28, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 29, 5, 1] 0\n", - "[60, 58, 10, 2] 4\n", - "[90, 87, 15, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (90, 87, 15, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 30, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 30, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 30, 1, 1] -8\n", - "[60, 60, 2, 2] -8\n", - "[90, 90, 3, 3] 0\n", - "[120, 120, 4, 4] -8\n", - "[150, 150, 5, 5] 0\n", - "[180, 180, 6, 6] 0\n", - "[210, 210, 7, 7] -8\n", - "[240, 240, 8, 8] 0\n", - "[270, 270, 9, 9] 0\n", - "[300, 300, 10, 10] -4\n", - "[330, 330, 11, 11] 8\n", - "[360, 360, 12, 12] 0\n", - "[390, 390, 13, 13] 0\n", - "[420, 420, 14, 14] 8\n", - "[450, 450, 15, 15] 0\n", - "[480, 480, 16, 16] 4\n", - "[510, 510, 17, 17] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (510, 510, 17, 17)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 510\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = -8\n", - "Sigma = -5849/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 510\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 12\n", - "Sigma = 5641/83 ~ 67\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 31, 12, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 31, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 32, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 32, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 33, 40, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 33, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 34, 16, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 34, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 35, 34, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 35, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 36, 8, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 36, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 36, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 36, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 39, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 39, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 39, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 39, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 40, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 40, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 40, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (30, 40, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5701/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 0, 6, 1] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 0, 6, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 1, 6, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 1, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 1, 28, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 1, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 2, 17, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 2, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 3, 25, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 3, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 4, 36, 0] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 4, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 5, 12, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 5, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 7, 1, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 7, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 8, 4, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 8, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 8, 10, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 8, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 9, 38, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 9, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 13, 11, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 13, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 14, 27, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 14, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 15, 26, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 15, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 15, 29, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 15, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 17, 18, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 17, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 18, 32, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 18, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 18, 39, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 18, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 19, 8, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 19, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 19, 27, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 19, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 20, 41, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 20, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 21, 12, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 21, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 22, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 22, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 24, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 24, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 24, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 24, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 26, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 26, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 27, 10, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 27, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 30, 40, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 30, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 31, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 31, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 31, 1, 1] -8\n", - "[62, 62, 2, 2] -4\n", - "[93, 93, 3, 3] -4\n", - "[124, 124, 4, 4] -8\n", - "[155, 155, 5, 5] 0\n", - "[186, 186, 6, 6] 0\n", - "[217, 217, 7, 7] -8\n", - "[248, 248, 8, 8] 4\n", - "[279, 279, 9, 9] -4\n", - "[310, 310, 10, 10] 0\n", - "[341, 341, 11, 11] 4\n", - "[372, 372, 12, 12] -4\n", - "[403, 403, 13, 13] 8\n", - "[434, 434, 14, 14] 4\n", - "[465, 465, 15, 15] -4\n", - "[496, 496, 16, 16] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (496, 496, 16, 16)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 496\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 81 * (83 - 81 )/83 =\n", - " = -83 + 162 * (2 )/83 =\n", - " = -83 + 162 * 2/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 496\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 81 * (83 - 81 )/83 =\n", - " = -83 + 162 * (2 )/83 =\n", - " = -83 + 162 * 2/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 12\n", - "Sigma = 5741/83 ~ 69\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 32, 8, 1] 4\n", - "[62, 64, 16, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (62, 64, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 62 * (83 - 62 )/83 =\n", - " = -83 + 124 * (21 )/83 =\n", - " = -83 + 124 * 21/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 32, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 32, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 34, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 34, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 34, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 34, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 35, 4, 1] 0\n", - "[62, 70, 8, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (62, 70, 8, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 62 * (83 - 62 )/83 =\n", - " = -83 + 124 * (21 )/83 =\n", - " = -83 + 124 * 21/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = -16\n", - "Sigma = -5613/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 70 * (83 - 70 )/83 =\n", - " = -83 + 140 * (13 )/83 =\n", - " = -83 + 140 * 13/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 36, 2, 1] -4\n", - "[62, 72, 4, 2] 4\n", - "[93, 108, 6, 3] -8\n", - "[124, 144, 8, 4] 0\n", - "[155, 180, 10, 5] 8\n", - "[186, 216, 12, 6] 4\n", - "[217, 252, 14, 7] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (217, 252, 14, 7)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 217\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 51 * (83 - 51 )/83 =\n", - " = -83 + 102 * (32 )/83 =\n", - " = -83 + 102 * 32/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 252\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 36, 13, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 36, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 37, 34, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 37, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 38, 20, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 38, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 38, 22, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 38, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 39, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 39, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 40, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (31, 40, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 2, 15, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 2, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 3, 8, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 3, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 3, 27, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 3, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 5, 9, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 5, 9, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 6, 3, 1] 8\n", - "[64, 12, 6, 2] 8\n", - "[96, 18, 9, 3] 0\n", - "[128, 24, 12, 4] 4\n", - "[160, 30, 15, 5] 4\n", - "[192, 36, 18, 6] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (192, 36, 18, 6)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 192\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = -20\n", - "Sigma = -5585/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 7, 41, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 7, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 8, 6, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 8, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 8, 28, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 8, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 11, 29, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 11, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 11, 33, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 11, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 12, 38, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 12, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 13, 15, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 13, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 14, 13, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 14, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 15, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 15, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 16, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 16, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 17, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 17, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 18, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 18, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 19, 1, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 19, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 20, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 20, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 20, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 20, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 21, 9, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 21, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 22, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 22, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 23, 2, 1] -8\n", - "[64, 46, 4, 2] -4\n", - "[96, 69, 6, 3] 0\n", - "[128, 92, 8, 4] 8\n", - "[160, 115, 10, 5] -4\n", - "[192, 138, 12, 6] 8\n", - "[224, 161, 14, 7] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (224, 161, 14, 7)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 224\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 58 * (83 - 58 )/83 =\n", - " = -83 + 116 * (25 )/83 =\n", - " = -83 + 116 * 25/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 161\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 23, 13, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 23, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 24, 36, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 24, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 25, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 25, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 25, 10, 1] 4\n", - "[64, 50, 20, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (64, 50, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 50 * (83 - 50 )/83 =\n", - " = -83 + 100 * (33 )/83 =\n", - " = -83 + 100 * 33/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 26, 20, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 26, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 27, 11, 1] 8\n", - "[64, 54, 22, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (64, 54, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 27, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 27, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 28, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 28, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 28, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 28, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 31, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 31, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 32, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 32, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 32, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 32, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 33, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 33, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 34, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 34, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 35, 6, 1] 0\n", - "[64, 70, 12, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (64, 70, 12, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 70 * (83 - 70 )/83 =\n", - " = -83 + 140 * (13 )/83 =\n", - " = -83 + 140 * 13/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 36, 40, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 36, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 39, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 39, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 40, 24, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 40, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 41, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (32, 41, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5949/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 1, 18, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 1, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 2, 24, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 2, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 2, 34, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 2, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 3, 0, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 3, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 4, 16, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 4, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 5, 4, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 5, 4, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 6, 21, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 6, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 6, 39, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 6, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 7, 17, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 7, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 10, 16, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 10, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 11, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 11, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 11, 32, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 11, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 12, 36, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 12, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 13, 34, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 13, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 14, 41, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 14, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 15, 7, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 15, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 16, 9, 1] 8\n", - "[66, 32, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (66, 32, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 17, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 17, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 17, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 17, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 18, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 18, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 20, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 20, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 21, 4, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 21, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 21, 10, 1] 8\n", - "[66, 42, 20, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (66, 42, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 22, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 22, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 23, 41, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 23, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 24, 20, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 24, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 24, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 24, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 26, 13, 1] 8\n", - "[66, 52, 26, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (66, 52, 26, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 52 * (83 - 52 )/83 =\n", - " = -83 + 104 * (31 )/83 =\n", - " = -83 + 104 * 31/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 28, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 28, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 28, 39, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 28, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 29, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 29, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 30, 12, 1] 8\n", - "[66, 60, 24, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (66, 60, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = -12\n", - "Sigma = -5641/83 ~ -67\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 31, 11, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 31, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 33, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 33, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 33, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 33, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 34, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 34, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 36, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 36, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 37, 23, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 37, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 38, 40, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 38, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 39, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 39, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 41, 26, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 41, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 41, 29, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (33, 41, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = -28\n", - "Sigma = -5913/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 0, 16, 1] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 0, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 1, 16, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 1, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 2, 29, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 2, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 2, 33, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 2, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 3, 4, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 3, 4, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 4, 40, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 4, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 5, 23, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 5, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 8, 30, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 8, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 9, 2, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 9, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 10, 40, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 10, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 11, 25, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 11, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 12, 20, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 12, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 13, 3, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 13, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 13, 33, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 13, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 14, 6, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 14, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 14, 28, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 14, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 15, 27, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 15, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 18, 9, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 18, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 19, 6, 1] 4\n", - "[68, 38, 12, 2] 8\n", - "[102, 57, 18, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (102, 57, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 57\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 57 * (83 - 57 )/83 =\n", - " = -83 + 114 * (26 )/83 =\n", - " = -83 + 114 * 26/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 20, 18, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 20, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 21, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 21, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 22, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 22, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 23, 11, 1] 8\n", - "[68, 46, 22, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (68, 46, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 23, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 23, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 24, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 24, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 25, 36, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 25, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 28, 25, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 28, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 29, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 29, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 30, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 30, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 33, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 33, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 33, 10, 1] 4\n", - "[68, 66, 20, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (68, 66, 20, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 68 * (83 - 68 )/83 =\n", - " = -83 + 136 * (15 )/83 =\n", - " = -83 + 136 * 15/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -5845/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 34, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 34, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 34, 1, 1] -8\n", - "[68, 68, 2, 2] -4\n", - "[102, 102, 3, 3] -4\n", - "[136, 136, 4, 4] -4\n", - "[170, 170, 5, 5] 4\n", - "[204, 204, 6, 6] -8\n", - "[238, 238, 7, 7] 0\n", - "[272, 272, 8, 8] -4\n", - "[306, 306, 9, 9] -4\n", - "[340, 340, 10, 10] 4\n", - "[374, 374, 11, 11] -4\n", - "[408, 408, 12, 12] 8\n", - "[442, 442, 13, 13] 0\n", - "[476, 476, 14, 14] 0\n", - "[510, 510, 15, 15] 8\n", - "[544, 544, 16, 16] 0\n", - "[578, 578, 17, 17] 8\n", - "[612, 612, 18, 18] 4\n", - "[646, 646, 19, 19] 4\n", - "[680, 680, 20, 20] 8\n", - "[714, 714, 21, 21] 0\n", - "[748, 748, 22, 22] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (748, 748, 22, 22)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 748\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 748\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[34, 35, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 35, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 35, 30, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 35, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 37, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 37, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 38, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 38, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 39, 38, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 39, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 40, 14, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 40, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 40, 19, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 40, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 41, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 41, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 41, 39, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (34, 41, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 0, 41, 1] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 0, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 1, 41, 0] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 1, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 2, 5, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 2, 5, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 3, 14, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 3, 14, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 3, 19, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 3, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 4, 6, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 4, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 4, 28, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 4, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 7, 22, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 7, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 7, 30, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 7, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 8, 1, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 8, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 10, 11, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 10, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 10, 28, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 10, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 11, 15, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 11, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 12, 9, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 12, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 13, 40, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 13, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 14, 36, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 14, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 16, 32, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 16, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 16, 39, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 16, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 17, 12, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 17, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 18, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 18, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 19, 7, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 19, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 22, 16, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 22, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 23, 36, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 23, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 24, 4, 1] -4\n", - "[70, 48, 8, 2] 0\n", - "[105, 72, 12, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (105, 72, 12, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = -20\n", - "Sigma = -5865/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 25, 8, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 25, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 25, 27, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 25, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 26, 38, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 26, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 27, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 27, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 29, 23, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 29, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 30, 16, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 30, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 31, 20, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 31, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 31, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 31, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 32, 7, 1] 0\n", - "[70, 64, 14, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (70, 64, 14, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 70 * (83 - 70 )/83 =\n", - " = -83 + 140 * (13 )/83 =\n", - " = -83 + 140 * 13/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -6065/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 32, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 32, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 33, 14, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 33, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 33, 23, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 33, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 35, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 35, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 35, 1, 1] -8\n", - "[70, 70, 2, 2] -4\n", - "[105, 105, 3, 3] -8\n", - "[140, 140, 4, 4] -4\n", - "[175, 175, 5, 5] 0\n", - "[210, 210, 6, 6] -8\n", - "[245, 245, 7, 7] 4\n", - "[280, 280, 8, 8] -4\n", - "[315, 315, 9, 9] 0\n", - "[350, 350, 10, 10] 0\n", - "[385, 385, 11, 11] 0\n", - "[420, 420, 12, 12] 8\n", - "[455, 455, 13, 13] -4\n", - "[490, 490, 14, 14] 4\n", - "[525, 525, 15, 15] 0\n", - "[560, 560, 16, 16] 8\n", - "[595, 595, 17, 17] 8\n", - "[630, 630, 18, 18] 4\n", - "[665, 665, 19, 19] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (665, 665, 19, 19)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 665\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 665\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 37, 12, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 37, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 39, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 39, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 40, 25, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 40, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 41, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (35, 41, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 0, 38, 1] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 0, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 1, 38, 0] -31\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 1, 38, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 2, 6, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 2, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 2, 28, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 2, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 3, 37, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 3, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 4, 7, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 4, 7, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 4, 31, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 4, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 6, 20, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 6, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 6, 22, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 6, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 7, 9, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 7, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 9, 14, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 9, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 9, 23, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 9, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 10, 7, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 10, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 11, 30, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 11, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 12, 29, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 12, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 12, 33, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 12, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 13, 6, 1] 8\n", - "[72, 26, 12, 2] 4\n", - "[108, 39, 18, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (108, 39, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 14, 35, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 14, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 15, 3, 1] 0\n", - "[72, 30, 6, 2] -4\n", - "[108, 45, 9, 3] 4\n", - "[144, 60, 12, 4] 8\n", - "[180, 75, 15, 5] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (180, 75, 15, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 180\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -5953/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 75 * (83 - 75 )/83 =\n", - " = -83 + 150 * (8 )/83 =\n", - " = -83 + 150 * 8/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 16, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 16, 17, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 18, 5, 1] 0\n", - "[72, 36, 10, 2] 4\n", - "[108, 54, 15, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (108, 54, 15, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5649/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 19, 12, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 19, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 20, 10, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 20, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 21, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 21, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 23, 8, 1] 4\n", - "[72, 46, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (72, 46, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 23, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 23, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 24, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 24, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 24, 39, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 24, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 25, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 25, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 26, 25, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 26, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 28, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 28, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 28, 30, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 28, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 29, 25, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 29, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 31, 9, 1] 4\n", - "[72, 62, 18, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (72, 62, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 62 * (83 - 62 )/83 =\n", - " = -83 + 124 * (21 )/83 =\n", - " = -83 + 124 * 21/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 32, 12, 1] 8\n", - "[72, 64, 24, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (72, 64, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 72 * (83 - 72 )/83 =\n", - " = -83 + 144 * (11 )/83 =\n", - " = -83 + 144 * 11/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = -8\n", - "Sigma = -5969/83 ~ -71\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 64 * (83 - 64 )/83 =\n", - " = -83 + 128 * (19 )/83 =\n", - " = -83 + 128 * 19/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 34, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 34, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 34, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 34, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 35, 26, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 35, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 36, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 36, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 36, 1, 1] -8\n", - "[72, 72, 2, 2] -4\n", - "[108, 108, 3, 3] -8\n", - "[144, 144, 4, 4] -4\n", - "[180, 180, 5, 5] 0\n", - "[216, 216, 6, 6] -8\n", - "[252, 252, 7, 7] 0\n", - "[288, 288, 8, 8] -8\n", - "[324, 324, 9, 9] 0\n", - "[360, 360, 10, 10] 0\n", - "[396, 396, 11, 11] 4\n", - "[432, 432, 12, 12] 4\n", - "[468, 468, 13, 13] 0\n", - "[504, 504, 14, 14] 8\n", - "[540, 540, 15, 15] -4\n", - "[576, 576, 16, 16] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (576, 576, 16, 16)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 576\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 576\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 12\n", - "Sigma = 5741/83 ~ 69\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 38, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 38, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 39, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (36, 39, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5829/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 1, 25, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 1, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 3, 36, 0] -39\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 3, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 4, 15, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 4, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 5, 20, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 5, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 6, 24, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 6, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 7, 3, 1] 4\n", - "[74, 14, 6, 2] 0\n", - "[111, 21, 9, 3] 4\n", - "[148, 28, 12, 4] 8\n", - "[185, 35, 15, 5] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (185, 35, 15, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 185\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -5785/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 8, 40, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 8, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 9, 17, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 9, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 9, 37, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 9, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 10, 15, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 10, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 11, 9, 1] 8\n", - "[74, 22, 18, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (74, 22, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 12, 41, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 12, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 16, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 16, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 17, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 17, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 20, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 20, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 20, 39, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 20, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 21, 20, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 21, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 21, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 21, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 22, 19, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 22, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 22, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 22, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 24, 11, 1] 4\n", - "[74, 48, 22, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (74, 48, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 24, 28, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 24, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 25, 2, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 25, 2, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 25, 13, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 25, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 27, 5, 1] -4\n", - "[74, 54, 10, 2] 0\n", - "[111, 81, 15, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (111, 81, 15, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 111\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = -24\n", - "Sigma = -5801/83 ~ -69\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 81 * (83 - 81 )/83 =\n", - " = -83 + 162 * (2 )/83 =\n", - " = -83 + 162 * 2/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 30, 14, 1] 8\n", - "[74, 60, 28, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (74, 60, 28, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 30, 19, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 30, 19, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 31, 16, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 31, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 32, 30, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 32, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 34, 6, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 34, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 34, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 34, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 35, 40, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 35, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 36, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 36, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 36, 33, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 36, 33, 0)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 37, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 37, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 37, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 37, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 38, 18, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 38, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 39, 22, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 39, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 39, 30, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 39, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 40, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 40, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 41, 8, 1] 0\n", - "[74, 82, 16, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (74, 82, 16, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 74 * (83 - 74 )/83 =\n", - " = -83 + 148 * (9 )/83 =\n", - " = -83 + 148 * 9/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = -8\n", - "Sigma = -6221/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 41, 35, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (37, 41, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 0, 36, 1] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 0, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 1, 36, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 1, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 3, 15, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 3, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 5, 18, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 5, 18, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 6, 2, 1] 4\n", - "[76, 12, 4, 2] 0\n", - "[114, 18, 6, 3] 0\n", - "[152, 24, 8, 4] 0\n", - "[190, 30, 10, 5] 4\n", - "[228, 36, 12, 6] 8\n", - "[266, 42, 14, 7] 8\n", - "[304, 48, 16, 8] 8\n", - "[342, 54, 18, 9] 4\n", - "[380, 60, 20, 10] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (380, 60, 20, 10)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 380\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5853/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 8\n", - "Sigma = 6093/83 ~ 73\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 6, 13, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 6, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 7, 4, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 7, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 7, 10, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 7, 10, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 8, 23, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 8, 23, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 9, 7, 1] 8\n", - "[76, 18, 14, 2] 8\n", - "[114, 27, 21, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (114, 27, 21, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 114\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 9, 31, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 9, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 10, 20, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 10, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 12, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 12, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 12, 32, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 12, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 14, 9, 1] 8\n", - "[76, 28, 18, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (76, 28, 18, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 15, 21, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 15, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 15, 39, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 15, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 17, 16, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 17, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 20, 6, 1] 0\n", - "[76, 40, 12, 2] 4\n", - "[114, 60, 18, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (114, 60, 18, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 114\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 21, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 21, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 22, 6, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 22, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 22, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 22, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 23, 9, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 23, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 25, 26, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 25, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 25, 29, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 25, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 26, 35, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 26, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 27, 38, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 27, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 28, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 28, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 29, 12, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 29, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 30, 11, 1] 4\n", - "[76, 60, 22, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (76, 60, 22, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 60 * (83 - 60 )/83 =\n", - " = -83 + 120 * (23 )/83 =\n", - " = -83 + 120 * 23/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 30, 28, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 30, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 31, 4, 1] -8\n", - "[76, 62, 8, 2] 0\n", - "[114, 93, 12, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (114, 93, 12, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 114\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = -24\n", - "Sigma = -5657/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 32, 24, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 32, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 33, 12, 1] 4\n", - "[76, 66, 24, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (76, 66, 24, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 76 * (83 - 76 )/83 =\n", - " = -83 + 152 * (7 )/83 =\n", - " = -83 + 152 * 7/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = -4\n", - "Sigma = -6157/83 ~ -74\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 34, 25, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 34, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 35, 14, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 35, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 35, 23, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 35, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 37, 3, 1] -8\n", - "[76, 74, 6, 2] 4\n", - "[114, 111, 9, 3] 4\n", - "[152, 148, 12, 4] 8\n", - "[190, 185, 15, 5] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (190, 185, 15, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 190\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = -20\n", - "Sigma = -5717/83 ~ -68\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 185\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 38, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 38, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 38, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 38, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 39, 24, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 39, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 39, 34, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (38, 39, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6125/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 2, 12, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 2, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 3, 27, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 3, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 5, 9, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 5, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 6, 3, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 6, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 6, 33, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 6, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = 5965/83 ~ 71\n", - "Satellite part = 4\n", - "Sigma = 6297/83 ~ 75\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 7, 40, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 7, 40, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 8, 11, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 8, 11, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 8, 28, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 8, 28, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 11, 26, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 11, 26, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 11, 29, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 11, 29, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 13, 15, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 13, 15, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 14, 2, 1] -4\n", - "[78, 28, 4, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (78, 28, 4, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 78 * (83 - 78 )/83 =\n", - " = -83 + 156 * (5 )/83 =\n", - " = -83 + 156 * 5/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = -4\n", - "Sigma = -6441/83 ~ -77\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 14, 13, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 14, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 15, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 15, 38, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = -3469/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3469/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 16, 8, 1] 4\n", - "[78, 32, 16, 2] 4\n", - "[117, 48, 24, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (117, 48, 24, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 117\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 48 * (83 - 48 )/83 =\n", - " = -83 + 96 * (35 )/83 =\n", - " = -83 + 96 * 35/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 16, 35, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 16, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 18, 7, 1] 0\n", - "[78, 36, 14, 2] 4\n", - "[117, 54, 21, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (117, 54, 21, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 117\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 54 * (83 - 54 )/83 =\n", - " = -83 + 108 * (29 )/83 =\n", - " = -83 + 108 * 29/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 18, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 18, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = 4549/83 ~ 54\n", - "Satellite part = 8\n", - "Sigma = 5213/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 19, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 19, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 20, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 20, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 21, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 21, 0, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 23, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 23, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 24, 36, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 24, 36, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = 4057/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 5053/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 25, 10, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 25, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 26, 20, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 26, 20, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 26, 22, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 26, 22, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 27, 11, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 27, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 28, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 28, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 28, 33, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 28, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 29, 20, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 29, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = 3757/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5085/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 30, 25, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 30, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 31, 41, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 31, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 32, 1, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 32, 1, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 34, 36, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 34, 36, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = 3557/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5217/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = -3505/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3505/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 35, 6, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 35, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 35, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 35, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 36, 5, 1] -4\n", - "[78, 72, 10, 2] 4\n", - "[117, 108, 15, 3] 8\n", - "[156, 144, 20, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (156, 144, 20, 4)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 156\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 73 * (83 - 73 )/83 =\n", - " = -83 + 146 * (10 )/83 =\n", - " = -83 + 146 * 10/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = -8\n", - "Sigma = -6093/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 144\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 61 * (83 - 61 )/83 =\n", - " = -83 + 122 * (22 )/83 =\n", - " = -83 + 122 * 22/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 38, 16, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 38, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 39, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 39, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 39, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 39, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 41, 24, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 41, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 41, 34, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (39, 41, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 0, 12, 1] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 0, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 1, 12, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 1, 12, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 2, 8, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 2, 8, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 2, 27, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 2, 27, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 3, 22, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 3, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 3, 30, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 3, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 4, 34, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 4, 34, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 5, 13, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 5, 13, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 7, 21, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 7, 21, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 7, 39, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 7, 39, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 8, 37, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 8, 37, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 9, 15, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 9, 15, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = -4849/83 ~ -58\n", - "Satellite part = 0\n", - "Sigma = -4849/83 ~ -58\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 10, 24, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 10, 24, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 10, 34, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 10, 34, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = 5429/83 ~ 65\n", - "Satellite part = 4\n", - "Sigma = 5761/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3557/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 11, 4, 1] 0\n", - "[80, 22, 8, 2] -8\n", - "[120, 33, 12, 3] 0\n", - "[160, 44, 16, 4] 8\n", - "[200, 55, 20, 5] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (200, 55, 20, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 200\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 34 * (83 - 34 )/83 =\n", - " = -83 + 68 * (49 )/83 =\n", - " = -83 + 68 * 49/83 = \n", - " = -83 + 3332/83 = \n", - " = -3557/83 \n", - "Pattern part = -3557/83 ~ -42\n", - "Satellite part = -28\n", - "Sigma = -5881/83 ~ -70\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 55\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 55 * (83 - 55 )/83 =\n", - " = -83 + 110 * (28 )/83 =\n", - " = -83 + 110 * 28/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 12, 11, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 12, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 13, 8, 1] 8\n", - "[80, 26, 16, 2] 0\n", - "[120, 39, 24, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (120, 39, 24, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6141/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 13, 35, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 13, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 14, 16, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 14, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 15, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 15, 6, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 15, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 15, 28, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = -3809/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3809/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 16, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 16, 20, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 17, 10, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 17, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 19, 16, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 19, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = 4457/83 ~ 53\n", - "Satellite part = 12\n", - "Sigma = 5453/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 21, 2, 1] -8\n", - "[80, 42, 4, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (80, 42, 4, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 42 * (83 - 42 )/83 =\n", - " = -83 + 84 * (41 )/83 =\n", - " = -83 + 84 * 41/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 21, 13, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 21, 13, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = 4285/83 ~ 51\n", - "Satellite part = 12\n", - "Sigma = 5281/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = -5069/83 ~ -61\n", - "Satellite part = 0\n", - "Sigma = -5069/83 ~ -61\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 23, 3, 1] -8\n", - "[80, 46, 6, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (80, 46, 6, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = -4\n", - "Sigma = -6741/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 46 * (83 - 46 )/83 =\n", - " = -83 + 92 * (37 )/83 =\n", - " = -83 + 92 * 37/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 25, 41, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 25, 41, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 30, 31, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 30, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 31, 5, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 31, 5, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = -6109/83 ~ -73\n", - "Satellite part = 0\n", - "Sigma = -6109/83 ~ -73\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 31, 21, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 31, 21, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 33, 30, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 33, 30, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = 3589/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4917/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 35, 17, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 35, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 35, 37, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 35, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = 3529/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5189/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 36, 19, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 36, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 36, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 36, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 38, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 38, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 38, 33, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 38, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 39, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 39, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 40, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 40, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 40, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 40, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = 3449/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5109/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 41, 9, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (40, 41, 9, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = -5557/83 ~ -66\n", - "Satellite part = 0\n", - "Sigma = -5557/83 ~ -66\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 0, 35, 1] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 0, 35, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 0\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 1, 8, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 1, 8, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = -5689/83 ~ -68\n", - "Satellite part = 0\n", - "Sigma = -5689/83 ~ -68\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 1, 35, 0] -35\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 1, 35, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 35 * (83 - 35 )/83 =\n", - " = -83 + 70 * (48 )/83 =\n", - " = -83 + 70 * 48/83 = \n", - " = -83 + 3360/83 = \n", - " = -3529/83 \n", - "Pattern part = -3529/83 ~ -42\n", - "Satellite part = 0\n", - "Sigma = -3529/83 ~ -42\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 4, 24, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 4, 24, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = 6257/83 ~ 75\n", - "Satellite part = 4\n", - "Sigma = 6589/83 ~ 79\n", - "\n", - "3. T(2, 83), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 24 * (83 - 24 )/83 =\n", - " = -83 + 48 * (59 )/83 =\n", - " = -83 + 48 * 59/83 = \n", - " = -83 + 2832/83 = \n", - " = -4057/83 \n", - "Pattern part = -4057/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -4057/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 5, 2, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 5, 2, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = -6565/83 ~ -79\n", - "Satellite part = 0\n", - "Sigma = -6565/83 ~ -79\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 6, 4, 1] 8\n", - "[82, 12, 8, 2] 0\n", - "[123, 18, 12, 3] 4\n", - "[164, 24, 16, 4] 4\n", - "[205, 30, 20, 5] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (205, 30, 20, 5)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 205\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6113/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = -4369/83 ~ -52\n", - "Satellite part = 0\n", - "Sigma = -4369/83 ~ -52\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 5 * (83 - 5 )/83 =\n", - " = -83 + 10 * (78 )/83 =\n", - " = -83 + 10 * 78/83 = \n", - " = -83 + 780/83 = \n", - " = -6109/83 \n", - "Pattern part = 6109/83 ~ 73\n", - "Satellite part = 4\n", - "Sigma = 6441/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 7, 19, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 7, 19, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 19 * (83 - 19 )/83 =\n", - " = -83 + 38 * (64 )/83 =\n", - " = -83 + 38 * 64/83 = \n", - " = -83 + 2432/83 = \n", - " = -4457/83 \n", - "Pattern part = -4457/83 ~ -53\n", - "Satellite part = 0\n", - "Sigma = -4457/83 ~ -53\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 7, 32, 0] -43\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 7, 32, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = 5825/83 ~ 70\n", - "Satellite part = 4\n", - "Sigma = 6157/83 ~ 74\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 8, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 8, 25, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 8 * (83 - 8 )/83 =\n", - " = -83 + 16 * (75 )/83 =\n", - " = -83 + 16 * 75/83 = \n", - " = -83 + 1200/83 = \n", - " = -5689/83 \n", - "Pattern part = 5689/83 ~ 68\n", - "Satellite part = 4\n", - "Sigma = 6021/83 ~ 72\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 9, 12, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 9, 12, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 9 * (83 - 9 )/83 =\n", - " = -83 + 18 * (74 )/83 =\n", - " = -83 + 18 * 74/83 = \n", - " = -83 + 1332/83 = \n", - " = -5557/83 \n", - "Pattern part = 5557/83 ~ 66\n", - "Satellite part = 4\n", - "Sigma = 5889/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = -5185/83 ~ -62\n", - "Satellite part = 0\n", - "Sigma = -5185/83 ~ -62\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 11, 10, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 11, 10, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = 5305/83 ~ 63\n", - "Satellite part = 4\n", - "Sigma = 5637/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 10 * (83 - 10 )/83 =\n", - " = -83 + 20 * (73 )/83 =\n", - " = -83 + 20 * 73/83 = \n", - " = -83 + 1460/83 = \n", - " = -5429/83 \n", - "Pattern part = -5429/83 ~ -65\n", - "Satellite part = 0\n", - "Sigma = -5429/83 ~ -65\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 12, 17, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 12, 17, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 17 * (83 - 17 )/83 =\n", - " = -83 + 34 * (66 )/83 =\n", - " = -83 + 34 * 66/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = -4645/83 ~ -55\n", - "Satellite part = 0\n", - "Sigma = -4645/83 ~ -55\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 12, 37, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 12, 37, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 12 * (83 - 12 )/83 =\n", - " = -83 + 24 * (71 )/83 =\n", - " = -83 + 24 * 71/83 = \n", - " = -83 + 1704/83 = \n", - " = -5185/83 \n", - "Pattern part = 5185/83 ~ 62\n", - "Satellite part = 8\n", - "Sigma = 5849/83 ~ 70\n", - "\n", - "3. T(2, 83), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = -3485/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3485/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 13, 27, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 13, 27, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 13 * (83 - 13 )/83 =\n", - " = -83 + 26 * (70 )/83 =\n", - " = -83 + 26 * 70/83 = \n", - " = -83 + 1820/83 = \n", - " = -5069/83 \n", - "Pattern part = 5069/83 ~ 61\n", - "Satellite part = 8\n", - "Sigma = 5733/83 ~ 69\n", - "\n", - "3. T(2, 83), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = -3865/83 ~ -46\n", - "Satellite part = 0\n", - "Sigma = -3865/83 ~ -46\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 14, 3, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 14, 3, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = -6409/83 ~ -77\n", - "Satellite part = 0\n", - "Sigma = -6409/83 ~ -77\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 14, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 14, 33, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = 4957/83 ~ 59\n", - "Satellite part = 8\n", - "Sigma = 5621/83 ~ 67\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 15, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 15, 11, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 15 * (83 - 15 )/83 =\n", - " = -83 + 30 * (68 )/83 =\n", - " = -83 + 30 * 68/83 = \n", - " = -83 + 2040/83 = \n", - " = -4849/83 \n", - "Pattern part = 4849/83 ~ 58\n", - "Satellite part = 8\n", - "Sigma = 5513/83 ~ 66\n", - "\n", - "3. T(2, 83), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 11 * (83 - 11 )/83 =\n", - " = -83 + 22 * (72 )/83 =\n", - " = -83 + 22 * 72/83 = \n", - " = -83 + 1584/83 = \n", - " = -5305/83 \n", - "Pattern part = -5305/83 ~ -63\n", - "Satellite part = 0\n", - "Sigma = -5305/83 ~ -63\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 16, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 16, 22, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = -4205/83 ~ -50\n", - "Satellite part = 0\n", - "Sigma = -4205/83 ~ -50\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 16, 30, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 16, 30, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = 4745/83 ~ 57\n", - "Satellite part = 8\n", - "Sigma = 5409/83 ~ 65\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 19, 3, 1] -4\n", - "[82, 38, 6, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (82, 38, 6, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 6 * (83 - 6 )/83 =\n", - " = -83 + 12 * (77 )/83 =\n", - " = -83 + 12 * 77/83 = \n", - " = -83 + 924/83 = \n", - " = -5965/83 \n", - "Pattern part = -5965/83 ~ -71\n", - "Satellite part = 0\n", - "Sigma = -5965/83 ~ -71\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 20, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 20, 31, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 20 * (83 - 20 )/83 =\n", - " = -83 + 40 * (63 )/83 =\n", - " = -83 + 40 * 63/83 = \n", - " = -83 + 2520/83 = \n", - " = -4369/83 \n", - "Pattern part = 4369/83 ~ 52\n", - "Satellite part = 12\n", - "Sigma = 5365/83 ~ 64\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 22, 7, 1] 0\n", - "[82, 44, 14, 2] 0\n", - "[123, 66, 21, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (123, 66, 21, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 123\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 66 * (83 - 66 )/83 =\n", - " = -83 + 132 * (17 )/83 =\n", - " = -83 + 132 * 17/83 = \n", - " = -83 + 2244/83 = \n", - " = -4645/83 \n", - "Pattern part = 4645/83 ~ 55\n", - "Satellite part = 8\n", - "Sigma = 5309/83 ~ 63\n", - "\n", - "3. T(2, 83), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 21 * (83 - 21 )/83 =\n", - " = -83 + 42 * (62 )/83 =\n", - " = -83 + 42 * 62/83 = \n", - " = -83 + 2604/83 = \n", - " = -4285/83 \n", - "Pattern part = -4285/83 ~ -51\n", - "Satellite part = 0\n", - "Sigma = -4285/83 ~ -51\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 22, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 22, 31, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 22 * (83 - 22 )/83 =\n", - " = -83 + 44 * (61 )/83 =\n", - " = -83 + 44 * 61/83 = \n", - " = -83 + 2684/83 = \n", - " = -4205/83 \n", - "Pattern part = 4205/83 ~ 50\n", - "Satellite part = 12\n", - "Sigma = 5201/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = -3665/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3665/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 23, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 23, 29, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 29 * (83 - 29 )/83 =\n", - " = -83 + 58 * (54 )/83 =\n", - " = -83 + 58 * 54/83 = \n", - " = -83 + 3132/83 = \n", - " = -3757/83 \n", - "Pattern part = -3757/83 ~ -45\n", - "Satellite part = 0\n", - "Sigma = -3757/83 ~ -45\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 23, 33, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 23, 33, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = 4129/83 ~ 49\n", - "Satellite part = 12\n", - "Sigma = 5125/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 33 * (83 - 33 )/83 =\n", - " = -83 + 66 * (50 )/83 =\n", - " = -83 + 66 * 50/83 = \n", - " = -83 + 3300/83 = \n", - " = -3589/83 \n", - "Pattern part = -3589/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3589/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 25, 40, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 25, 40, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = 3989/83 ~ 48\n", - "Satellite part = 12\n", - "Sigma = 4985/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3449/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 26, 18, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 26, 18, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = 3925/83 ~ 47\n", - "Satellite part = 12\n", - "Sigma = 4921/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 18 * (83 - 18 )/83 =\n", - " = -83 + 36 * (65 )/83 =\n", - " = -83 + 36 * 65/83 = \n", - " = -83 + 2340/83 = \n", - " = -4549/83 \n", - "Pattern part = -4549/83 ~ -54\n", - "Satellite part = 0\n", - "Sigma = -4549/83 ~ -54\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 27, 25, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 27, 25, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 27 * (83 - 27 )/83 =\n", - " = -83 + 54 * (56 )/83 =\n", - " = -83 + 54 * 56/83 = \n", - " = -83 + 3024/83 = \n", - " = -3865/83 \n", - "Pattern part = 3865/83 ~ 46\n", - "Satellite part = 16\n", - "Sigma = 5193/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 25 * (83 - 25 )/83 =\n", - " = -83 + 50 * (58 )/83 =\n", - " = -83 + 50 * 58/83 = \n", - " = -83 + 2900/83 = \n", - " = -3989/83 \n", - "Pattern part = -3989/83 ~ -48\n", - "Satellite part = 0\n", - "Sigma = -3989/83 ~ -48\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 28, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 28, 4, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 28 * (83 - 28 )/83 =\n", - " = -83 + 56 * (55 )/83 =\n", - " = -83 + 56 * 55/83 = \n", - " = -83 + 3080/83 = \n", - " = -3809/83 \n", - "Pattern part = 3809/83 ~ 45\n", - "Satellite part = 16\n", - "Sigma = 5137/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 4 * (83 - 4 )/83 =\n", - " = -83 + 8 * (79 )/83 =\n", - " = -83 + 8 * 79/83 = \n", - " = -83 + 632/83 = \n", - " = -6257/83 \n", - "Pattern part = -6257/83 ~ -75\n", - "Satellite part = 0\n", - "Sigma = -6257/83 ~ -75\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 28, 10, 1] 4\n", - "[82, 56, 20, 2] 8\n", - "[123, 84, 30, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (123, 84, 30, 3)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 123\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 40 * (83 - 40 )/83 =\n", - " = -83 + 80 * (43 )/83 =\n", - " = -83 + 80 * 43/83 = \n", - " = -83 + 3440/83 = \n", - " = -3449/83 \n", - "Pattern part = -3449/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6105/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "3. T(2, 83), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = -3709/83 ~ -44\n", - "Satellite part = 0\n", - "Sigma = -3709/83 ~ -44\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 3 * (83 - 3 )/83 =\n", - " = -83 + 6 * (80 )/83 =\n", - " = -83 + 6 * 80/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 30, 7, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 30, 7, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 30 * (83 - 30 )/83 =\n", - " = -83 + 60 * (53 )/83 =\n", - " = -83 + 60 * 53/83 = \n", - " = -83 + 3180/83 = \n", - " = -3709/83 \n", - "Pattern part = 3709/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 5037/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 7 * (83 - 7 )/83 =\n", - " = -83 + 14 * (76 )/83 =\n", - " = -83 + 14 * 76/83 = \n", - " = -83 + 1064/83 = \n", - " = -5825/83 \n", - "Pattern part = -5825/83 ~ -70\n", - "Satellite part = 0\n", - "Sigma = -5825/83 ~ -70\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 31, 32, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 31, 32, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = -3625/83 ~ -43\n", - "Satellite part = 0\n", - "Sigma = -3625/83 ~ -43\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 31, 39, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 31, 39, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 31 * (83 - 31 )/83 =\n", - " = -83 + 62 * (52 )/83 =\n", - " = -83 + 62 * 52/83 = \n", - " = -83 + 3224/83 = \n", - " = -3665/83 \n", - "Pattern part = 3665/83 ~ 44\n", - "Satellite part = 16\n", - "Sigma = 4993/83 ~ 60\n", - "\n", - "3. T(2, 83), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = -3457/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3457/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 32, 16, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 32, 16, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 32 * (83 - 32 )/83 =\n", - " = -83 + 64 * (51 )/83 =\n", - " = -83 + 64 * 51/83 = \n", - " = -83 + 3264/83 = \n", - " = -3625/83 \n", - "Pattern part = 3625/83 ~ 43\n", - "Satellite part = 16\n", - "Sigma = 4953/83 ~ 59\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 36, 14, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 36, 14, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 14 * (83 - 14 )/83 =\n", - " = -83 + 28 * (69 )/83 =\n", - " = -83 + 28 * 69/83 = \n", - " = -83 + 1932/83 = \n", - " = -4957/83 \n", - "Pattern part = -4957/83 ~ -59\n", - "Satellite part = 0\n", - "Sigma = -4957/83 ~ -59\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 36, 23, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 36, 23, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 36 * (83 - 36 )/83 =\n", - " = -83 + 72 * (47 )/83 =\n", - " = -83 + 72 * 47/83 = \n", - " = -83 + 3384/83 = \n", - " = -3505/83 \n", - "Pattern part = 3505/83 ~ 42\n", - "Satellite part = 20\n", - "Sigma = 5165/83 ~ 62\n", - "\n", - "3. T(2, 83), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 23 * (83 - 23 )/83 =\n", - " = -83 + 46 * (60 )/83 =\n", - " = -83 + 46 * 60/83 = \n", - " = -83 + 2760/83 = \n", - " = -4129/83 \n", - "Pattern part = -4129/83 ~ -49\n", - "Satellite part = 0\n", - "Sigma = -4129/83 ~ -49\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 37, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 37, 41, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 37 * (83 - 37 )/83 =\n", - " = -83 + 74 * (46 )/83 =\n", - " = -83 + 74 * 46/83 = \n", - " = -83 + 3404/83 = \n", - " = -3485/83 \n", - "Pattern part = 3485/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5145/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = 0\n", - "Sigma = -3445/83 ~ -41\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 38, 26, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 38, 26, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 38 * (83 - 38 )/83 =\n", - " = -83 + 76 * (45 )/83 =\n", - " = -83 + 76 * 45/83 = \n", - " = -83 + 3420/83 = \n", - " = -3469/83 \n", - "Pattern part = 3469/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5129/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 39, 16, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 39, 16, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 39 * (83 - 39 )/83 =\n", - " = -83 + 78 * (44 )/83 =\n", - " = -83 + 78 * 44/83 = \n", - " = -83 + 3432/83 = \n", - " = -3457/83 \n", - "Pattern part = 3457/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5117/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 16 * (83 - 16 )/83 =\n", - " = -83 + 32 * (67 )/83 =\n", - " = -83 + 32 * 67/83 = \n", - " = -83 + 2144/83 = \n", - " = -4745/83 \n", - "Pattern part = -4745/83 ~ -57\n", - "Satellite part = 0\n", - "Sigma = -4745/83 ~ -57\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 40, 13, 1] 8\n", - "[82, 80, 26, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (82, 80, 26, 2)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 82 * (83 - 82 )/83 =\n", - " = -83 + 164 * (1 )/83 =\n", - " = -83 + 164 * 1/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 80 * (83 - 80 )/83 =\n", - " = -83 + 160 * (3 )/83 =\n", - " = -83 + 160 * 3/83 = \n", - " = -83 + 480/83 = \n", - " = -6409/83 \n", - "Pattern part = 6409/83 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 6409/83 ~ 77\n", - "\n", - "3. T(2, 83), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 26 * (83 - 26 )/83 =\n", - " = -83 + 52 * (57 )/83 =\n", - " = -83 + 52 * 57/83 = \n", - " = -83 + 2964/83 = \n", - " = -3925/83 \n", - "Pattern part = -3925/83 ~ -47\n", - "Satellite part = 0\n", - "Sigma = -3925/83 ~ -47\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 2 * (83 - 2 )/83 =\n", - " = -83 + 4 * (81 )/83 =\n", - " = -83 + 4 * 81/83 = \n", - " = -83 + 324/83 = \n", - " = -6565/83 \n", - "Pattern part = 6565/83 ~ 79\n", - "Satellite part = 0\n", - "Sigma = 6565/83 ~ 79\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 41, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 41, 0, 0)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 0\n", - "4. -T(2, 13; 2, 83), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 41, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "and theta vector: (41, 41, 1, 1)\n", - "\n", - "1. T(2, 17; 2, 83), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = -3445/83 ~ -41\n", - "Satellite part = -32\n", - "Sigma = -6101/83 ~ -73\n", - "\n", - "2. -T(2, 11; 2, 83), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 41 * (83 - 41 )/83 =\n", - " = -83 + 82 * (42 )/83 =\n", - " = -83 + 82 * 42/83 = \n", - " = -83 + 3444/83 = \n", - " = -3445/83 \n", - "Pattern part = 3445/83 ~ 41\n", - "Satellite part = 20\n", - "Sigma = 5105/83 ~ 61\n", - "\n", - "3. T(2, 83), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = -6725/83 ~ -81\n", - "Satellite part = 0\n", - "Sigma = -6725/83 ~ -81\n", - "\n", - "4. -T(2, 13; 2, 83), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -83 + 2 * 1 * (83 - 1 )/83 =\n", - " = -83 + 2 * (82 )/83 =\n", - " = -83 + 2 * 82/83 = \n", - " = -83 + 164/83 = \n", - " = -6725/83 \n", - "Pattern part = 6725/83 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 6725/83 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 0, 1, 1] 0\n", - "[0, 0, 2, 2] 0\n", - "[0, 0, 3, 3] 0\n", - "[0, 0, 4, 4] 0\n", - "[0, 0, 5, 5] 0\n", - "[0, 0, 6, 6] 0\n", - "[0, 0, 7, 7] 0\n", - "[0, 0, 8, 8] 0\n", - "[0, 0, 9, 9] 0\n", - "[0, 0, 10, 10] 4\n", - "[0, 0, 11, 11] 4\n", - "[0, 0, 12, 12] 0\n", - "[0, 0, 13, 13] 0\n", - "[0, 0, 14, 14] 0\n", - "[0, 0, 15, 15] 0\n", - "[0, 0, 16, 16] 4\n", - "[0, 0, 17, 17] 4\n", - "[0, 0, 18, 18] 4\n", - "[0, 0, 19, 19] 4\n", - "[0, 0, 20, 20] 0\n", - "[0, 0, 21, 21] 0\n", - "[0, 0, 22, 22] 4\n", - "[0, 0, 23, 23] 4\n", - "[0, 0, 24, 24] 4\n", - "[0, 0, 25, 25] 4\n", - "[0, 0, 26, 26] 4\n", - "[0, 0, 27, 27] 4\n", - "[0, 0, 28, 28] 4\n", - "[0, 0, 29, 29] 4\n", - "[0, 0, 30, 30] 4\n", - "[0, 0, 31, 31] 4\n", - "[0, 0, 32, 32] 4\n", - "[0, 0, 33, 33] 4\n", - "[0, 0, 34, 34] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 0, 34, 34)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 24\n", - "Sigma = 8389/103 ~ 81\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 1, 1, 0] 0\n", - "[0, 2, 2, 0] 0\n", - "[0, 3, 3, 0] 0\n", - "[0, 4, 4, 0] -4\n", - "[0, 5, 5, 0] -4\n", - "[0, 6, 6, 0] -4\n", - "[0, 7, 7, 0] -4\n", - "[0, 8, 8, 0] -4\n", - "[0, 9, 9, 0] -4\n", - "[0, 10, 10, 0] -4\n", - "[0, 11, 11, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 1, 38, 1] 127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 1, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 2, 2, 0] 0\n", - "[0, 4, 4, 0] -4\n", - "[0, 6, 6, 0] -4\n", - "[0, 8, 8, 0] -4\n", - "[0, 10, 10, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 3, 3, 0] 0\n", - "[0, 6, 6, 0] -4\n", - "[0, 9, 9, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 4, 4, 0] -4\n", - "[0, 8, 8, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 4, 29, 1] 119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 4, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 5, 5, 0] -4\n", - "[0, 10, 10, 0] -4\n", - "[0, 15, 15, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 15, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 5, 51, 1] 119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 5, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 6, 6, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 7, 7, 0] -4\n", - "[0, 14, 14, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 14, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 7, 16, 1] 107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 7, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 8, 8, 0] -4\n", - "[0, 16, 16, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 16, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 9, 9, 0] -4\n", - "[0, 18, 18, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 18, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 9, 44, 1] 111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 9, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 10, 10, 0] -4\n", - "[0, 20, 20, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 20, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 11, 11, 0] -4\n", - "[0, 22, 22, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 22, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 11, 15, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 11, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 12, 12, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 12, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 13, 13, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 13, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 14, 14, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 14, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 15, 15, 0] -8\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 15, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 16, 16, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 16, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 17, 17, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 17, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 18, 4, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 18, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 18, 18, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 18, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 19, 19, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 19, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 20, 20, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 20, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 20, 35, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 20, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 21, 21, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 21, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 21, 37, 1] 95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 21, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 22, 22, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 22, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 23, 18, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 23, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 23, 23, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 23, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 24, 24, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 24, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 25, 25, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 25, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 25, 27, 1] 91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 25, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 26, 26, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 26, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 26, 33, 1] 91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 26, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 27, 3, 1] 67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 27, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 27, 27, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 27, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 28, 8, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 28, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 28, 28, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 28, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 29, 11, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 29, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 29, 29, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 29, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 30, 30, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 30, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 31, 31, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 31, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 32, 32, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 32, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 32, 43, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 32, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 33, 33, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 33, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 33, 36, 1] 83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 33, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 34, 34, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 34, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 35, 14, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 35, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 35, 35, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 35, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 36, 24, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 36, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 36, 36, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 36, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 37, 37, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 37, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 38, 38, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 38, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 39, 39, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 39, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 40, 40, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 40, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 40, 46, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 40, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 41, 31, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 41, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 41, 41, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 41, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 42, 23, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 42, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 42, 42, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 42, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 43, 43, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 43, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 44, 17, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 44, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 44, 44, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 44, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 45, 45, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 45, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 46, 46, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 46, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 47, 47, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 47, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 48, 48, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 48, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 49, 41, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 49, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 49, 49, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 49, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 50, 21, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 50, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 50, 50, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 50, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 51, 51, 0] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (0, 51, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 0\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 0, 0, 1] 0\n", - "[2, 0, 0, 2] 0\n", - "[3, 0, 0, 3] 0\n", - "[4, 0, 0, 4] 4\n", - "[5, 0, 0, 5] 0\n", - "[6, 0, 0, 6] 0\n", - "[7, 0, 0, 7] 0\n", - "[8, 0, 0, 8] 0\n", - "[9, 0, 0, 9] 0\n", - "[10, 0, 0, 10] 4\n", - "[11, 0, 0, 11] 4\n", - "[12, 0, 0, 12] 4\n", - "[13, 0, 0, 13] 4\n", - "[14, 0, 0, 14] 4\n", - "[15, 0, 0, 15] 0\n", - "[16, 0, 0, 16] 4\n", - "[17, 0, 0, 17] 4\n", - "[18, 0, 0, 18] 4\n", - "[19, 0, 0, 19] 4\n", - "[20, 0, 0, 20] 4\n", - "[21, 0, 0, 21] 4\n", - "[22, 0, 0, 22] 8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 0, 0, 22)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 16\n", - "Sigma = 8693/103 ~ 84\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 1, 0, 0] 0\n", - "[2, 2, 0, 0] 0\n", - "[3, 3, 0, 0] 0\n", - "[4, 4, 0, 0] 0\n", - "[5, 5, 0, 0] -4\n", - "[6, 6, 0, 0] -4\n", - "[7, 7, 0, 0] -4\n", - "[8, 8, 0, 0] -4\n", - "[9, 9, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[11, 11, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[13, 13, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[15, 15, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 15, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 1, 1, 1] 0\n", - "[2, 2, 2, 2] 0\n", - "[3, 3, 3, 3] 0\n", - "[4, 4, 4, 4] 0\n", - "[5, 5, 5, 5] -4\n", - "[6, 6, 6, 6] -4\n", - "[7, 7, 7, 7] -4\n", - "[8, 8, 8, 8] -4\n", - "[9, 9, 9, 9] -4\n", - "[10, 10, 10, 10] 0\n", - "[11, 11, 11, 11] 0\n", - "[12, 12, 12, 12] -4\n", - "[13, 13, 13, 13] -4\n", - "[14, 14, 14, 14] -4\n", - "[15, 15, 15, 15] -8\n", - "[16, 16, 16, 16] -4\n", - "[17, 17, 17, 17] -4\n", - "[18, 18, 18, 18] -4\n", - "[19, 19, 19, 19] -4\n", - "[20, 20, 20, 20] -8\n", - "[21, 21, 21, 21] -8\n", - "[22, 22, 22, 22] -4\n", - "[23, 23, 23, 23] -4\n", - "[24, 24, 24, 24] -8\n", - "[25, 25, 25, 25] -8\n", - "[26, 26, 26, 26] -8\n", - "[27, 27, 27, 27] -8\n", - "[28, 28, 28, 28] -8\n", - "[29, 29, 29, 29] -8\n", - "[30, 30, 30, 30] -8\n", - "[31, 31, 31, 31] -8\n", - "[32, 32, 32, 32] -8\n", - "[33, 33, 33, 33] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 33, 33, 33)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 20\n", - "Sigma = 8049/103 ~ 78\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 2, 2, 1] 0\n", - "[2, 4, 4, 2] -4\n", - "[3, 6, 6, 3] -4\n", - "[4, 8, 8, 4] 0\n", - "[5, 10, 10, 5] -4\n", - "[6, 12, 12, 6] -8\n", - "[7, 14, 14, 7] -8\n", - "[8, 16, 16, 8] -8\n", - "[9, 18, 18, 9] -8\n", - "[10, 20, 20, 10] -8\n", - "[11, 22, 22, 11] -8\n", - "[12, 24, 24, 12] -8\n", - "[13, 26, 26, 13] -8\n", - "[14, 28, 28, 14] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 28, 28, 14)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 8\n", - "Sigma = 8941/103 ~ 86\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 3, 3, 1] 0\n", - "[2, 6, 6, 2] -4\n", - "[3, 9, 9, 3] -4\n", - "[4, 12, 12, 4] -4\n", - "[5, 15, 15, 5] -8\n", - "[6, 18, 18, 6] -8\n", - "[7, 21, 21, 7] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 21, 21, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 3, 27, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 3, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 4, 4, 1] -4\n", - "[2, 8, 8, 2] -4\n", - "[3, 12, 12, 3] -8\n", - "[4, 16, 16, 4] -4\n", - "[5, 20, 20, 5] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 20, 20, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 4, 18, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 4, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 5, 5, 1] -4\n", - "[2, 10, 10, 2] -4\n", - "[3, 15, 15, 3] -8\n", - "[4, 20, 20, 4] -8\n", - "[5, 25, 25, 5] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 25, 25, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 6, 6, 1] -4\n", - "[2, 12, 12, 2] -8\n", - "[3, 18, 18, 3] -8\n", - "[4, 24, 24, 4] -8\n", - "[5, 30, 30, 5] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 30, 30, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 7, 7, 1] -4\n", - "[2, 14, 14, 2] -8\n", - "[3, 21, 21, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 21, 21, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 8, 8, 1] -4\n", - "[2, 16, 16, 2] -8\n", - "[3, 24, 24, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 24, 24, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 8, 28, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 8, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 9, 9, 1] -4\n", - "[2, 18, 18, 2] -8\n", - "[3, 27, 27, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 27, 27, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 10, 10, 1] -4\n", - "[2, 20, 20, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 20, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 11, 11, 1] -4\n", - "[2, 22, 22, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 22, 22, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 11, 29, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 11, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 12, 12, 1] -8\n", - "[2, 24, 24, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 24, 24, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 13, 13, 1] -8\n", - "[2, 26, 26, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 26, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 14, 14, 1] -8\n", - "[2, 28, 28, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 28, 28, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 14, 35, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 14, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 15, 11, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 15, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 15, 15, 1] -8\n", - "[2, 30, 30, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 30, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 16, 7, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 16, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 16, 16, 1] -8\n", - "[2, 32, 32, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 32, 32, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 17, 17, 1] -8\n", - "[2, 34, 34, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 34, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 17, 44, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 17, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 18, 18, 1] -8\n", - "[2, 36, 36, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 36, 36, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 18, 23, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 18, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 19, 19, 1] -8\n", - "[2, 38, 38, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 38, 38, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 20, 20, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 20, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 21, 21, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 21, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 21, 50, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 21, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 22, 22, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 22, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 23, 23, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 23, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 23, 42, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 23, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 24, 24, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 24, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 24, 36, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 24, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 25, 25, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 25, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 26, 26, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 26, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 27, 25, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 27, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 27, 27, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 27, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 28, 28, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 28, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 29, 4, 0] -139\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 29, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 29, 29, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 29, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 30, 30, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 30, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 31, 31, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 31, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 31, 41, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 31, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 32, 32, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 32, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 33, 26, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 33, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 33, 33, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 33, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 34, 34, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 34, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 35, 20, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 35, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 35, 35, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 35, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 36, 33, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 36, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 36, 36, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 36, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 37, 21, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 37, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 37, 37, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 37, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 38, 1, 0] -147\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 38, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 38, 38, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 38, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 39, 39, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 39, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 40, 40, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 40, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 41, 41, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 41, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 41, 49, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 41, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 42, 42, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 42, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 43, 32, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 43, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 43, 43, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 43, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 44, 9, 0] -139\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 44, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 44, 44, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 44, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 45, 45, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 45, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 46, 40, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 46, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 46, 46, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 46, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 47, 47, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 47, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 48, 48, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 48, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 49, 49, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 49, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 50, 50, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 50, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 51, 5, 0] -147\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 51, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 51, 51, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (1, 51, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 0, 10, 1] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 0, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 1, 10, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 1, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 2, 0, 0] 0\n", - "[4, 4, 0, 0] 0\n", - "[6, 6, 0, 0] -4\n", - "[8, 8, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[16, 16, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 16, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 2, 1, 1] 0\n", - "[4, 4, 2, 2] 0\n", - "[6, 6, 3, 3] -4\n", - "[8, 8, 4, 4] -4\n", - "[10, 10, 5, 5] -4\n", - "[12, 12, 6, 6] -4\n", - "[14, 14, 7, 7] -4\n", - "[16, 16, 8, 8] -8\n", - "[18, 18, 9, 9] -8\n", - "[20, 20, 10, 10] -4\n", - "[22, 22, 11, 11] -4\n", - "[24, 24, 12, 12] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 12, 12)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 8\n", - "Sigma = 9249/103 ~ 89\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 4, 42, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 4, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 6, 41, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 6, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 6, 49, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 6, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 7, 47, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 7, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 8, 24, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 8, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 8, 36, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 8, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 10, 32, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 10, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 11, 18, 1] 4\n", - "[4, 22, 36, 2] -4\n", - "[6, 33, 54, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 33, 54, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 11, 23, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 11, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 12, 48, 1] 8\n", - "[4, 24, 96, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 24, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 13, 28, 1] 4\n", - "[4, 26, 56, 2] -8\n", - "[6, 39, 84, 3] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 39, 84, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 15, 4, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 15, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 15, 18, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 15, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 16, 47, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 16, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 17, 39, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 17, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 19, 7, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 19, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 21, 5, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 21, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 21, 51, 1] -4\n", - "[4, 42, 102, 2] -44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 42, 102, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 22, 45, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 22, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 24, 26, 1] -8\n", - "[4, 48, 52, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 48, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 25, 2, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 25, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 26, 40, 1] -8\n", - "[4, 52, 80, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 52, 80, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 27, 2, 0] -135\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 27, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 28, 33, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 28, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 28, 36, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 28, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 29, 23, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 29, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 29, 42, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 29, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 30, 22, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 30, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 31, 37, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 31, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 32, 14, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 32, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 33, 40, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 33, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 33, 46, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 33, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 34, 15, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 34, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 36, 46, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 36, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 37, 51, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 37, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 39, 30, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 39, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 40, 19, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 40, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 41, 21, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 41, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 41, 37, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 41, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 42, 3, 0] -143\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 42, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 44, 39, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 44, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 45, 8, 0] -139\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 45, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 46, 19, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 46, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 48, 31, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 48, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 49, 21, 1] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 49, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 49, 50, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 49, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 50, 5, 1] -44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 50, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 51, 34, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (2, 51, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 2, 43, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 2, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 3, 0, 0] 0\n", - "[6, 6, 0, 0] -4\n", - "[9, 9, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[15, 15, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 15, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 3, 1, 1] 0\n", - "[6, 6, 2, 2] -4\n", - "[9, 9, 3, 3] -4\n", - "[12, 12, 4, 4] -4\n", - "[15, 15, 5, 5] -8\n", - "[18, 18, 6, 6] -8\n", - "[21, 21, 7, 7] -8\n", - "[24, 24, 8, 8] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 8, 8)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 4\n", - "Sigma = 9501/103 ~ 92\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 4, 25, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 4, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 4, 27, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 4, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 5, 4, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 5, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 5, 29, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 5, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 6, 50, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 6, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 7, 12, 1] 4\n", - "[6, 14, 24, 2] 4\n", - "[9, 21, 36, 3] 0\n", - "[12, 28, 48, 4] 0\n", - "[15, 35, 60, 5] -4\n", - "[18, 42, 72, 6] -8\n", - "[21, 49, 84, 7] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 49, 84, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 8, 40, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 8, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 8, 46, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 8, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 9, 22, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 9, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 10, 20, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 10, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 10, 35, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 10, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 11, 3, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 11, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 12, 41, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 12, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 12, 49, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 12, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 13, 26, 1] 8\n", - "[6, 26, 52, 2] -8\n", - "[9, 39, 78, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 39, 78, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 16, 12, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 16, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 18, 25, 1] 0\n", - "[6, 36, 50, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 36, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 20, 17, 1] -8\n", - "[6, 40, 34, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 40, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 20, 44, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 20, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 22, 8, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 22, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 22, 28, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 22, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 24, 19, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 24, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 26, 7, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 26, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 26, 16, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 26, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 27, 0, 1] 67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 27, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 28, 40, 1] -8\n", - "[6, 56, 80, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 56, 80, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 29, 3, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 29, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 29, 27, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 29, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 30, 45, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 30, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 31, 5, 0] -135\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 31, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 31, 51, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 31, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 33, 16, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 33, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 34, 18, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 34, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 34, 23, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 34, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 35, 17, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 35, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 36, 19, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 36, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 38, 32, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 38, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 40, 47, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 40, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 41, 5, 1] -40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 41, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 42, 2, 0] -143\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 42, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 45, 33, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 45, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 45, 36, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 45, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 47, 48, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 47, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 48, 21, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 48, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 48, 37, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 48, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 49, 34, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 49, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 50, 15, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 50, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 51, 11, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 51, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 51, 29, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (3, 51, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 2, 20, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 2, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 2, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 2, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 3, 32, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 3, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 4, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[16, 16, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 16, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 4, 1, 1] 0\n", - "[8, 8, 2, 2] -4\n", - "[12, 12, 3, 3] -4\n", - "[16, 16, 4, 4] -8\n", - "[20, 20, 5, 5] -8\n", - "[24, 24, 6, 6] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 6, 6)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 4\n", - "Sigma = 9857/103 ~ 95\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 5, 3, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 5, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 7, 31, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 7, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 7, 41, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 7, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 8, 7, 1] 0\n", - "[8, 16, 14, 2] -4\n", - "[12, 24, 21, 3] -4\n", - "[16, 32, 28, 4] -4\n", - "[20, 40, 35, 5] 0\n", - "[24, 48, 42, 6] -4\n", - "[28, 56, 49, 7] -4\n", - "[32, 64, 56, 8] 0\n", - "[36, 72, 63, 9] 4\n", - "[40, 80, 70, 10] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 80, 70, 10)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 8\n", - "Sigma = 9573/103 ~ 92\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 9, 13, 1] 4\n", - "[8, 18, 26, 2] 4\n", - "[12, 27, 39, 3] 0\n", - "[16, 36, 52, 4] -4\n", - "[20, 45, 65, 5] -4\n", - "[24, 54, 78, 6] -8\n", - "[28, 63, 91, 7] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 63, 91, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 63\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 91\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 91 * (103 - 91 )/103 =\n", - " = -103 + 182 * (12 )/103 =\n", - " = -103 + 182 * 12/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 11, 38, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 11, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 12, 5, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 12, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 12, 51, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 12, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 13, 16, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 13, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 15, 2, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 15, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 16, 31, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 16, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 17, 45, 1] 4\n", - "[8, 34, 90, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 34, 90, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 18, 0, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 18, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 19, 6, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 19, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 20, 30, 1] 0\n", - "[8, 40, 60, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 40, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 21, 23, 1] -4\n", - "[8, 42, 46, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 42, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 21, 42, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 21, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 22, 46, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 22, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 24, 47, 1] -4\n", - "[8, 48, 94, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 48, 94, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 29, 1, 0] -135\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 29, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 29, 38, 1] -8\n", - "[8, 58, 76, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 58, 76, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 30, 24, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 30, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 30, 36, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 30, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 31, 11, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 31, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 31, 15, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 31, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 32, 9, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 32, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 32, 44, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 32, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 34, 25, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 34, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 34, 27, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 34, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 35, 30, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 35, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 37, 18, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 37, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 37, 23, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 37, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 39, 8, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 39, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 39, 28, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 39, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 41, 11, 1] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 41, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 41, 29, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 41, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 42, 10, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 42, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 43, 17, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 43, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 43, 44, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 43, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 44, 13, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 44, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 45, 19, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 45, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 46, 12, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 46, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 47, 37, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 47, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 48, 34, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 48, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 49, 4, 0] -143\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 49, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 49, 29, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 49, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 50, 42, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (4, 50, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 0, 39, 1] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 0, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 1, 39, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 1, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 2, 17, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 2, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 2, 44, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 2, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 5, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[15, 15, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 15, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 5, 1, 1] -4\n", - "[10, 10, 2, 2] -4\n", - "[15, 15, 3, 3] -8\n", - "[20, 20, 4, 4] -8\n", - "[25, 25, 5, 5] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 25, 5, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 7, 5, 1] -4\n", - "[10, 14, 10, 2] 0\n", - "[15, 21, 15, 3] -4\n", - "[20, 28, 20, 4] 0\n", - "[25, 35, 25, 5] 0\n", - "[30, 42, 30, 6] 0\n", - "[35, 49, 35, 7] 0\n", - "[40, 56, 40, 8] 0\n", - "[45, 63, 45, 9] -4\n", - "[50, 70, 50, 10] 4\n", - "[55, 77, 55, 11] 8\n", - "[60, 84, 60, 12] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 84, 60, 12)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 8\n", - "Sigma = 9249/103 ~ 89\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 9, 46, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 9, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 10, 30, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 10, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 11, 32, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 11, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 12, 4, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 12, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 12, 29, 1] 8\n", - "[10, 24, 58, 2] 0\n", - "[15, 36, 87, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 36, 87, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 13, 12, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 13, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 14, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 14, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 15, 32, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 15, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 15, 43, 1] 8\n", - "[10, 30, 86, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 30, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 16, 5, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 16, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 16, 51, 1] 4\n", - "[10, 32, 102, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 32, 102, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 17, 26, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 17, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 17, 33, 1] 4\n", - "[10, 34, 66, 2] -8\n", - "[15, 51, 99, 3] -36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 51, 99, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 99\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 18, 14, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 18, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 19, 50, 1] 0\n", - "[10, 38, 100, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 38, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 20, 13, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 20, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 21, 2, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 21, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 23, 14, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 23, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 23, 35, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 23, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 24, 6, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 24, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 26, 31, 1] -8\n", - "[10, 52, 62, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 52, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 26, 41, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 26, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 28, 48, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 28, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 30, 19, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 30, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 31, 3, 0] -135\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 31, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 32, 22, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 32, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 33, 31, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 33, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 35, 45, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 35, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 36, 6, 1] -36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 36, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 38, 9, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 38, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 39, 40, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 39, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 40, 37, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 40, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 41, 3, 1] -40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 41, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 41, 27, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 41, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 42, 20, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 42, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 42, 35, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 42, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 44, 26, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 44, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 46, 49, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 46, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 48, 23, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 48, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 48, 42, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 48, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 49, 25, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 49, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 49, 27, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 49, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 50, 2, 1] -44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 50, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 51, 1, 0] -147\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 51, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 51, 38, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (5, 51, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 0, 45, 1] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 0, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 1, 45, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 1, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 2, 22, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 2, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 3, 30, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 3, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 4, 17, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 4, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 5, 14, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 5, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 5, 35, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 5, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 6, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 6, 1, 1] -4\n", - "[12, 12, 2, 2] -4\n", - "[18, 18, 3, 3] -8\n", - "[24, 24, 4, 4] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 4, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 7, 23, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 7, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 7, 42, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 7, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 8, 21, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 8, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 8, 50, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 8, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 9, 47, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 9, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 10, 8, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 10, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 13, 37, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 13, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 14, 26, 1] 8\n", - "[12, 28, 52, 2] 0\n", - "[18, 42, 78, 3] -8\n", - "[24, 56, 104, 4] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 56, 104, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 104\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 16, 18, 1] 0\n", - "[12, 32, 36, 2] -4\n", - "[18, 48, 54, 3] -8\n", - "[24, 64, 72, 4] 0\n", - "[30, 80, 90, 5] 4\n", - "[36, 96, 108, 6] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 96, 108, 6)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 4\n", - "Sigma = 9857/103 ~ 95\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 16, 23, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 16, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 18, 17, 1] -4\n", - "[12, 36, 34, 2] -4\n", - "[18, 54, 51, 3] -8\n", - "[24, 72, 68, 4] 8\n", - "[30, 90, 85, 5] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 90, 85, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 85\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 85 * (103 - 85 )/103 =\n", - " = -103 + 170 * (18 )/103 =\n", - " = -103 + 170 * 18/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 18, 44, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 18, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 19, 4, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 19, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 19, 29, 1] 0\n", - "[12, 38, 58, 2] -8\n", - "[18, 57, 87, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 57, 87, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 57\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 20, 40, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 20, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 20, 46, 1] 0\n", - "[12, 40, 92, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 40, 92, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 21, 32, 1] 0\n", - "[12, 42, 64, 2] -8\n", - "[18, 63, 96, 3] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 63, 96, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 63\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 22, 6, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 22, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 23, 9, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 23, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 23, 44, 1] -4\n", - "[12, 46, 88, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 46, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 24, 5, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 24, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 24, 51, 1] -4\n", - "[12, 48, 102, 2] -36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 48, 102, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 26, 34, 1] -4\n", - "[12, 52, 68, 2] -8\n", - "[18, 78, 102, 3] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 78, 102, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 27, 30, 1] -8\n", - "[12, 54, 60, 2] -8\n", - "[18, 81, 90, 3] -4\n", - "[24, 108, 120, 4] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 108, 120, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 28, 50, 1] -8\n", - "[12, 56, 100, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 56, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 30, 12, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 30, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 32, 24, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 32, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 33, 34, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 33, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 34, 20, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 34, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 35, 46, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 35, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 36, 5, 1] -36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 36, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 37, 32, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 37, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 37, 43, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 37, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 40, 15, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 40, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 41, 10, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 41, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[6, 42, 9, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 42, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 43, 28, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 43, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 44, 47, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 44, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 45, 41, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 45, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 45, 49, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 45, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 48, 38, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 48, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 49, 10, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 49, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 51, 14, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (6, 51, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 0, 40, 1] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 0, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 1, 40, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 1, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 1, 46, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 1, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 2, 26, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 2, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 2, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 2, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 3, 8, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 3, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 3, 28, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 3, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 5, 39, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 5, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 6, 20, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 6, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 7, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[21, 21, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 21, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 7, 1, 1] -4\n", - "[14, 14, 2, 2] -4\n", - "[21, 21, 3, 3] -8\n", - "[28, 28, 4, 4] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 28, 4, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 8, 4, 1] -4\n", - "[14, 16, 8, 2] 0\n", - "[21, 24, 12, 3] -4\n", - "[28, 32, 16, 4] 0\n", - "[35, 40, 20, 5] -4\n", - "[42, 48, 24, 6] 0\n", - "[49, 56, 28, 7] -4\n", - "[56, 64, 32, 8] 0\n", - "[63, 72, 36, 9] 4\n", - "[70, 80, 40, 10] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 80, 40, 10)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 8\n", - "Sigma = 9573/103 ~ 92\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 8, 18, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 8, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 9, 41, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 9, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 9, 49, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 9, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 10, 19, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 10, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 11, 22, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 11, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 13, 11, 1] 0\n", - "[14, 26, 22, 2] 0\n", - "[21, 39, 33, 3] 0\n", - "[28, 52, 44, 4] 0\n", - "[35, 65, 55, 5] 4\n", - "[42, 78, 66, 6] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 78, 66, 6)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 4\n", - "Sigma = 9857/103 ~ 95\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 13, 29, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 13, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 16, 1, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 16, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 16, 38, 1] 8\n", - "[14, 32, 76, 2] 0\n", - "[21, 48, 114, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 48, 114, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 114\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 17, 31, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 17, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 19, 2, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 19, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 21, 17, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 21, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 22, 34, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 22, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 23, 45, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 23, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 24, 42, 1] 0\n", - "[14, 48, 84, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 48, 84, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 25, 24, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 25, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 26, 3, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 26, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 27, 28, 1] -8\n", - "[14, 54, 56, 2] -8\n", - "[21, 81, 84, 3] 8\n", - "[28, 108, 112, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 108, 112, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 112\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 28, 18, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 28, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 28, 23, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 28, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 29, 22, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 29, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 30, 50, 1] -8\n", - "[14, 60, 100, 2] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 60, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 32, 7, 1] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 32, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 38, 46, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 38, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 39, 37, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 39, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 40, 25, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 40, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 42, 45, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 42, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 43, 7, 0] -135\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 43, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 43, 16, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 43, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 44, 31, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 44, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 44, 41, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 44, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 45, 15, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 45, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 46, 25, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 46, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 46, 27, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 46, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 47, 10, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 47, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 48, 14, 1] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 48, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 48, 35, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 48, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 50, 17, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 50, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 50, 44, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 50, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 51, 9, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (7, 51, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 1, 12, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 1, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 3, 7, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 3, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 4, 40, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 4, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 4, 46, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 4, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 5, 8, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 5, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 6, 30, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 6, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 8, 0, 0] -4\n", - "[16, 16, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 16, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 8, 1, 1] -4\n", - "[16, 16, 2, 2] -8\n", - "[24, 24, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 3, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 9, 11, 1] 8\n", - "[16, 18, 22, 2] 8\n", - "[24, 27, 33, 3] 8\n", - "[32, 36, 44, 4] 8\n", - "[40, 45, 55, 5] 4\n", - "[48, 54, 66, 6] 0\n", - "[56, 63, 77, 7] 0\n", - "[64, 72, 88, 8] -4\n", - "[72, 81, 99, 9] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 81, 99, 9)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 99\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 4\n", - "Sigma = 9329/103 ~ 90\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 9, 29, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 9, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 10, 6, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 10, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 11, 26, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 11, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 12, 9, 1] 0\n", - "[16, 24, 18, 2] 0\n", - "[24, 36, 27, 3] 0\n", - "[32, 48, 36, 4] 4\n", - "[40, 60, 45, 5] 4\n", - "[48, 72, 54, 6] 8\n", - "[56, 84, 63, 7] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (56, 84, 63, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 13, 38, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 13, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 14, 21, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 14, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 14, 37, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 14, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 15, 26, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 15, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 15, 33, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 15, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 17, 15, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 17, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 18, 40, 1] 8\n", - "[16, 36, 80, 2] -8\n", - "[24, 54, 120, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 54, 120, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 19, 20, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 19, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 19, 35, 1] 8\n", - "[16, 38, 70, 2] -4\n", - "[24, 57, 105, 3] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 57, 105, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 57\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 20, 50, 1] 4\n", - "[16, 40, 100, 2] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 40, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 21, 45, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 21, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 22, 3, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 22, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 22, 27, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 22, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 24, 10, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 24, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 25, 47, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 25, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 26, 32, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 26, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 26, 43, 1] 0\n", - "[16, 52, 86, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 52, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 28, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 28, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 29, 46, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 29, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 30, 42, 1] -4\n", - "[16, 60, 84, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 60, 84, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 32, 31, 1] -8\n", - "[16, 64, 62, 2] -4\n", - "[24, 96, 93, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 96, 93, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 32, 41, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 32, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 33, 43, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 33, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 34, 28, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 34, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 35, 21, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 35, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 35, 50, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 35, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 36, 10, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 36, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 38, 12, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 38, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 39, 4, 1] -36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 39, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 39, 18, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 39, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 41, 22, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 41, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 42, 19, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 42, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 43, 31, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 43, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 44, 11, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 44, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 44, 15, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 44, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 45, 2, 0] -139\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 45, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 49, 22, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 49, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 50, 45, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 50, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 51, 13, 1] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (8, 51, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 0, 34, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 0, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 1, 34, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 1, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 2, 51, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 2, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 3, 49, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 3, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 4, 48, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 4, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 6, 26, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 6, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 6, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 6, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 7, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 7, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 9, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 9, 1, 1] -4\n", - "[18, 18, 2, 2] -8\n", - "[27, 27, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 27, 3, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 10, 15, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 10, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 11, 12, 1] 4\n", - "[18, 22, 24, 2] 8\n", - "[27, 33, 36, 3] 4\n", - "[36, 44, 48, 4] 4\n", - "[45, 55, 60, 5] 4\n", - "[54, 66, 72, 6] 4\n", - "[63, 77, 84, 7] 8\n", - "[72, 88, 96, 8] 4\n", - "[81, 99, 108, 9] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (81, 99, 108, 9)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 4\n", - "Sigma = 9329/103 ~ 90\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 12, 8, 1] 0\n", - "[18, 24, 16, 2] 0\n", - "[27, 36, 24, 3] 0\n", - "[36, 48, 32, 4] 4\n", - "[45, 60, 40, 5] 4\n", - "[54, 72, 48, 6] 8\n", - "[63, 84, 56, 7] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (63, 84, 56, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 12, 28, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 12, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 14, 42, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 14, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 15, 12, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 15, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 16, 22, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 16, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 17, 38, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 17, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 18, 48, 1] 8\n", - "[18, 36, 96, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 36, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 21, 19, 1] 0\n", - "[18, 42, 38, 2] -4\n", - "[27, 63, 57, 3] 0\n", - "[36, 84, 76, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 84, 76, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 23, 6, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 23, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 24, 17, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 24, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 25, 21, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 25, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 25, 37, 1] 0\n", - "[18, 50, 74, 2] -8\n", - "[27, 75, 111, 3] -8\n", - "[36, 100, 148, 4] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 100, 148, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 148\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 26, 9, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 26, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 27, 37, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 27, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 30, 43, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 30, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 31, 46, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 31, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 32, 4, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 32, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 32, 29, 1] -8\n", - "[18, 64, 58, 2] -4\n", - "[27, 96, 87, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 96, 87, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 33, 9, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 33, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 33, 44, 1] -8\n", - "[18, 66, 88, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 66, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 34, 47, 1] -8\n", - "[18, 68, 94, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 68, 94, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 36, 17, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 36, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 36, 44, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 36, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 37, 19, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 37, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 38, 5, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 38, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 41, 40, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 41, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 41, 46, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 41, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 42, 6, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 42, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 43, 11, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 43, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 43, 29, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 43, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 44, 1, 0] -139\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 44, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 44, 38, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 44, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 45, 20, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 45, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 46, 39, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 46, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 47, 45, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 47, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 48, 24, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 48, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 48, 36, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 48, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 49, 40, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 49, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 50, 16, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 50, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 51, 7, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (9, 51, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 0, 2, 1] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 0, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 1, 2, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 1, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 2, 25, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 2, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 2, 27, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 2, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 3, 42, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 3, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 4, 15, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 4, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 5, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 5, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 5, 50, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 5, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 7, 19, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 7, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 8, 45, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 8, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 10, 0, 0] -4\n", - "[20, 20, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 20, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 10, 1, 1] -4\n", - "[20, 20, 2, 2] -8\n", - "[30, 30, 3, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 30, 3, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 14, 32, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 14, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 15, 34, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 15, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 18, 11, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 18, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 18, 15, 1] 0\n", - "[20, 36, 30, 2] 0\n", - "[30, 54, 45, 3] 0\n", - "[40, 72, 60, 4] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 72, 60, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 19, 40, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 19, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 19, 46, 1] 8\n", - "[20, 38, 92, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 38, 92, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 21, 41, 1] 8\n", - "[20, 42, 82, 2] -8\n", - "[30, 63, 123, 3] -4\n", - "[40, 84, 164, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 84, 164, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 164\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 61 * (103 - 61 )/103 =\n", - " = -103 + 122 * (42 )/103 =\n", - " = -103 + 122 * 42/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 21, 49, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 21, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 22, 30, 1] 4\n", - "[20, 44, 60, 2] 0\n", - "[30, 66, 90, 3] -8\n", - "[40, 88, 120, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 88, 120, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 23, 11, 1] -8\n", - "[20, 46, 22, 2] -8\n", - "[30, 69, 33, 3] 8\n", - "[40, 92, 44, 4] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 92, 44, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 23, 29, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 23, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 24, 8, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 24, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 26, 24, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 26, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 28, 13, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 28, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 30, 39, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 30, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 31, 48, 1] -4\n", - "[20, 62, 96, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 62, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 32, 10, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 32, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 33, 28, 1] -8\n", - "[20, 66, 56, 2] 0\n", - "[30, 99, 84, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 99, 84, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 34, 51, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 34, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 36, 8, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 36, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 36, 28, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 36, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 37, 31, 1] -8\n", - "[20, 74, 62, 2] 8\n", - "[30, 111, 93, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 111, 93, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 37, 41, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 37, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 39, 17, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 39, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 39, 44, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 39, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 40, 26, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 40, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 40, 33, 1] -8\n", - "[20, 80, 66, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 80, 66, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 41, 6, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 41, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 42, 4, 0] -135\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 42, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 42, 29, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 42, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 45, 22, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 45, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 46, 33, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 46, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 46, 36, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 46, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 47, 7, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 47, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 47, 16, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 47, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 48, 12, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 48, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 49, 6, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 49, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 50, 49, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 50, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 51, 21, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 51, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 51, 37, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (10, 51, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 5, 25, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 5, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 5, 27, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 5, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 6, 11, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 6, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 6, 15, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 6, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 7, 49, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 7, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 8, 47, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 8, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 9, 8, 1] 8\n", - "[22, 18, 16, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 18, 16, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 9, 28, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 9, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 10, 17, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 10, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 10, 44, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 10, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 11, 0, 0] -4\n", - "[22, 22, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 22, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 11, 1, 1] -4\n", - "[22, 22, 2, 2] -8\n", - "[33, 33, 3, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 33, 3, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 12, 34, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 12, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 13, 7, 1] 0\n", - "[22, 26, 14, 2] 0\n", - "[33, 39, 21, 3] -4\n", - "[44, 52, 28, 4] 0\n", - "[55, 65, 35, 5] 8\n", - "[66, 78, 42, 6] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 78, 42, 6)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 4\n", - "Sigma = 9857/103 ~ 95\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 14, 30, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 14, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 15, 1, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 15, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 15, 38, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 15, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 16, 41, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 16, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 16, 49, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 16, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 17, 13, 1] 0\n", - "[22, 34, 26, 2] 4\n", - "[33, 51, 39, 3] 0\n", - "[44, 68, 52, 4] 8\n", - "[55, 85, 65, 5] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (55, 85, 65, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 55\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 55 * (103 - 55 )/103 =\n", - " = -103 + 110 * (48 )/103 =\n", - " = -103 + 110 * 48/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 85\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 85 * (103 - 85 )/103 =\n", - " = -103 + 170 * (18 )/103 =\n", - " = -103 + 170 * 18/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 65\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 65 * (103 - 65 )/103 =\n", - " = -103 + 130 * (38 )/103 =\n", - " = -103 + 130 * 38/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 18, 10, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 18, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 19, 31, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 19, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 22, 40, 1] 8\n", - "[22, 44, 80, 2] -4\n", - "[33, 66, 120, 3] -4\n", - "[44, 88, 160, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 88, 160, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 160\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[11, 23, 10, 1] -8\n", - "[22, 46, 20, 2] -8\n", - "[33, 69, 30, 3] 4\n", - "[44, 92, 40, 4] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 92, 40, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 25, 14, 1] -8\n", - "[22, 50, 28, 2] -4\n", - "[33, 75, 42, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 75, 42, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 25, 35, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 25, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 26, 12, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 26, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 27, 14, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 27, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 28, 47, 1] 0\n", - "[22, 56, 94, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 56, 94, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 29, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 29, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 30, 26, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 30, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 30, 33, 1] 0\n", - "[22, 60, 66, 2] 0\n", - "[33, 90, 99, 3] 4\n", - "[44, 120, 132, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 120, 132, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 132\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 31, 4, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 31, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 31, 29, 1] -4\n", - "[22, 62, 58, 2] 0\n", - "[33, 93, 87, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 93, 87, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 32, 39, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 32, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 33, 12, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 33, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 37, 42, 1] -4\n", - "[22, 74, 84, 2] 4\n", - "[33, 111, 126, 3] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 111, 126, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 126\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 39, 24, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 39, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 40, 48, 1] -8\n", - "[22, 80, 96, 2] -4\n", - "[33, 120, 144, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 120, 144, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 41, 4, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 41, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 41, 18, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 41, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 42, 43, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 42, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 43, 9, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 43, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 44, 8, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 44, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 45, 16, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 45, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 46, 48, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 46, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 47, 21, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 47, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 47, 50, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 47, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 49, 18, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 49, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 49, 23, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 49, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 51, 3, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 51, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 51, 27, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (11, 51, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 0, 28, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 0, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 1, 8, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 1, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 1, 28, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 1, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 2, 13, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 2, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 3, 22, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 3, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 4, 39, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 4, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 6, 43, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 6, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 7, 3, 1] 8\n", - "[24, 14, 6, 2] 4\n", - "[36, 21, 9, 3] 4\n", - "[48, 28, 12, 4] 0\n", - "[60, 35, 15, 5] -4\n", - "[72, 42, 18, 6] -4\n", - "[84, 49, 21, 7] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 49, 21, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 7, 27, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 7, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 8, 34, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 8, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 9, 12, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 9, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 10, 33, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 10, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 10, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 10, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 11, 9, 1] 8\n", - "[24, 22, 18, 2] 8\n", - "[36, 33, 27, 3] 8\n", - "[48, 44, 36, 4] 4\n", - "[60, 55, 45, 5] 0\n", - "[72, 66, 54, 6] 4\n", - "[84, 77, 63, 7] 4\n", - "[96, 88, 72, 8] 0\n", - "[108, 99, 81, 9] 8\n", - "[120, 110, 90, 10] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (120, 110, 90, 10)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 110\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 8\n", - "Sigma = 9573/103 ~ 92\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 12, 0, 0] -4\n", - "[24, 24, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 12, 1, 1] -4\n", - "[24, 24, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 13, 5, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 13, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 13, 51, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 13, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 14, 19, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 14, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 15, 9, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 15, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 15, 44, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 15, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 16, 3, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 16, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 20, 16, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 20, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 21, 20, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 21, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 21, 35, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 21, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 22, 49, 1] 8\n", - "[24, 44, 98, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 44, 98, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 23, 30, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 23, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 26, 11, 1] -8\n", - "[24, 52, 22, 2] -8\n", - "[36, 78, 33, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 78, 33, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 26, 29, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 26, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 28, 34, 1] 4\n", - "[24, 56, 68, 2] 0\n", - "[36, 84, 102, 3] -4\n", - "[48, 112, 136, 4] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 112, 136, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 112\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 136\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 29, 39, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 29, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 30, 6, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 30, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 31, 32, 1] 0\n", - "[24, 62, 64, 2] 0\n", - "[36, 93, 96, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 93, 96, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 32, 46, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 32, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[12, 33, 11, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 33, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 33, 15, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 33, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 35, 19, 1] -8\n", - "[24, 70, 38, 2] 4\n", - "[36, 105, 57, 3] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 105, 57, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 36, 15, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 36, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 37, 14, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 37, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 37, 35, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 37, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 38, 8, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 38, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 39, 48, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 39, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 40, 18, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 40, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 40, 23, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 40, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 42, 30, 1] -8\n", - "[24, 84, 60, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 84, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 43, 26, 1] -8\n", - "[24, 86, 52, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 86, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 44, 12, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 44, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 45, 50, 1] -8\n", - "[24, 90, 100, 2] 4\n", - "[36, 135, 150, 3] 8\n", - "[48, 180, 200, 4] -4\n", - "[60, 225, 250, 5] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 225, 250, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 225\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 250\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 46, 4, 1] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 46, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 46, 18, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 46, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 48, 10, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 48, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 50, 20, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (12, 50, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 0, 48, 1] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 0, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 1, 48, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 1, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 2, 12, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 2, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 3, 47, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 3, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 5, 28, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 5, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 9, 4, 1] 4\n", - "[26, 18, 8, 2] 4\n", - "[39, 27, 12, 3] 0\n", - "[52, 36, 16, 4] 0\n", - "[65, 45, 20, 5] -4\n", - "[78, 54, 24, 6] -8\n", - "[91, 63, 28, 7] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (91, 63, 28, 7)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 91\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 91 * (103 - 91 )/103 =\n", - " = -103 + 182 * (12 )/103 =\n", - " = -103 + 182 * 12/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -4\n", - "Sigma = -8837/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 63\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 4\n", - "Sigma = 9677/103 ~ 93\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 9, 18, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 9, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 10, 31, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 10, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 11, 40, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 11, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 11, 46, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 11, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 12, 39, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 12, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 13, 0, 0] -4\n", - "[26, 26, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 26, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 13, 1, 1] -4\n", - "[26, 26, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 26, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 14, 50, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 14, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 15, 46, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 15, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 17, 11, 1] 4\n", - "[26, 34, 22, 2] 0\n", - "[39, 51, 33, 3] 4\n", - "[52, 68, 44, 4] 8\n", - "[65, 85, 55, 5] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (65, 85, 55, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 65\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 65 * (103 - 65 )/103 =\n", - " = -103 + 130 * (38 )/103 =\n", - " = -103 + 130 * 38/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 85\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 85 * (103 - 85 )/103 =\n", - " = -103 + 170 * (18 )/103 =\n", - " = -103 + 170 * 18/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 55\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 55 * (103 - 55 )/103 =\n", - " = -103 + 110 * (48 )/103 =\n", - " = -103 + 110 * 48/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 17, 29, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 17, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 18, 19, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 18, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 20, 5, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 20, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 20, 51, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 20, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 21, 13, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 21, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 22, 25, 1] 8\n", - "[26, 44, 50, 2] 0\n", - "[39, 66, 75, 3] 4\n", - "[52, 88, 100, 4] 8\n", - "[65, 110, 125, 5] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (65, 110, 125, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 65\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 65 * (103 - 65 )/103 =\n", - " = -103 + 130 * (38 )/103 =\n", - " = -103 + 130 * 38/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 110\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 125\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 23, 19, 1] 4\n", - "[26, 46, 38, 2] 0\n", - "[39, 69, 57, 3] 8\n", - "[52, 92, 76, 4] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 92, 76, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 24, 43, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 24, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 27, 47, 1] 4\n", - "[26, 54, 94, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 54, 94, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 28, 10, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 28, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 29, 40, 1] 4\n", - "[26, 58, 80, 2] -4\n", - "[39, 87, 120, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 87, 120, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 31, 22, 1] -4\n", - "[26, 62, 44, 2] 0\n", - "[39, 93, 66, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 93, 66, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 32, 49, 1] 0\n", - "[26, 64, 98, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 64, 98, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 33, 32, 1] 0\n", - "[26, 66, 64, 2] 4\n", - "[39, 99, 96, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 99, 96, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 34, 24, 1] -4\n", - "[26, 68, 48, 2] 4\n", - "[39, 102, 72, 3] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 102, 72, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 34, 36, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 34, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 35, 51, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 35, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 36, 32, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 36, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 36, 43, 1] 0\n", - "[26, 72, 86, 2] 0\n", - "[39, 108, 129, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 108, 129, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 37, 45, 1] -4\n", - "[26, 74, 90, 2] -4\n", - "[39, 111, 135, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 111, 135, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 135\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 39, 23, 1] -8\n", - "[26, 78, 46, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 78, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 39, 42, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 39, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 40, 14, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 40, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 40, 35, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 40, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 42, 16, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 42, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 43, 41, 1] -4\n", - "[26, 86, 82, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 86, 82, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 43, 49, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 43, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 44, 4, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 44, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 44, 29, 1] -8\n", - "[26, 88, 58, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 88, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 45, 38, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 45, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 46, 14, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 46, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 47, 17, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 47, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 48, 30, 1] -8\n", - "[26, 96, 60, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 96, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 50, 13, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 50, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 51, 8, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 51, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 51, 28, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (13, 51, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 2, 18, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 2, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 2, 23, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 2, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 3, 15, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 3, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 4, 51, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 4, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 5, 6, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 5, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 6, 47, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 6, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 7, 33, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 7, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 7, 36, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 7, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 9, 20, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 9, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 9, 35, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 9, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 10, 25, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 10, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 10, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 10, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 11, 21, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 11, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 11, 50, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 11, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 12, 19, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 12, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 13, 30, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 13, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 14, 0, 0] -4\n", - "[28, 28, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 28, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 14, 1, 1] -4\n", - "[28, 28, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 28, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 15, 21, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 15, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 15, 37, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 15, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 16, 24, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 16, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 16, 36, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 16, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 17, 14, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 17, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 18, 5, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 18, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 18, 51, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 18, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 19, 28, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 19, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 22, 17, 1] 4\n", - "[28, 44, 34, 2] 4\n", - "[42, 66, 51, 3] 8\n", - "[56, 88, 68, 4] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (56, 88, 68, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 22, 44, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 22, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 23, 5, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 23, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 24, 22, 1] 4\n", - "[28, 48, 44, 2] 0\n", - "[42, 72, 66, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 72, 66, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 25, 11, 1] -4\n", - "[28, 50, 22, 2] -4\n", - "[42, 75, 33, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 75, 33, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 25, 29, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 25, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 26, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 26, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 27, 11, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 27, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 27, 15, 1] -4\n", - "[28, 54, 30, 2] 0\n", - "[42, 81, 45, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 81, 45, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 29, 50, 1] 4\n", - "[28, 58, 100, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 58, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 32, 2, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 32, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 34, 31, 1] 0\n", - "[28, 68, 62, 2] 8\n", - "[42, 102, 93, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 102, 93, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 34, 41, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 34, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 35, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 35, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 37, 12, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 37, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 38, 42, 1] 0\n", - "[28, 76, 84, 2] 8\n", - "[42, 114, 126, 3] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 114, 126, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 126\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 40, 13, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 40, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 42, 34, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 42, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 44, 14, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 44, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 44, 35, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 44, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 45, 39, 1] -4\n", - "[28, 90, 78, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 90, 78, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 46, 13, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 46, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 47, 46, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 47, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 48, 7, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 48, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 50, 48, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 50, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 51, 6, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (14, 51, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 3, 14, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 3, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 4, 10, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 4, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 5, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 5, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 6, 11, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 6, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 6, 29, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 6, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 7, 37, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 7, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 8, 47, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 8, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 9, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 9, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 10, 9, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 10, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 10, 44, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 10, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 11, 0, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 11, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 12, 34, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 12, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 15, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 15, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 15, 1, 1] -8\n", - "[30, 30, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 30, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 16, 49, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 16, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 17, 8, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 17, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 18, 10, 1] 0\n", - "[30, 36, 20, 2] 0\n", - "[45, 54, 30, 3] 0\n", - "[60, 72, 40, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 72, 40, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 19, 31, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 19, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 19, 41, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 19, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 20, 22, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 20, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 23, 43, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 23, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 25, 20, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 25, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 25, 35, 1] 8\n", - "[30, 50, 70, 2] 4\n", - "[45, 75, 105, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 75, 105, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 27, 14, 1] -8\n", - "[30, 54, 28, 2] 0\n", - "[45, 81, 42, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 81, 42, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 27, 35, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 27, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 30, 26, 1] 0\n", - "[30, 60, 52, 2] 4\n", - "[45, 90, 78, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 90, 78, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 31, 4, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 31, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 31, 18, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 31, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 32, 39, 1] 0\n", - "[30, 64, 78, 2] 4\n", - "[45, 96, 117, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 96, 117, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 117\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 33, 12, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 33, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 34, 2, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 34, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 36, 12, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 36, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 39, 24, 1] -8\n", - "[30, 78, 48, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 78, 48, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 39, 36, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 39, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 40, 6, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 40, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 41, 18, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 41, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 41, 23, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 41, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 42, 32, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 42, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 42, 43, 1] -4\n", - "[30, 84, 86, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 84, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 43, 39, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 43, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 44, 8, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 44, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 44, 28, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 44, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 45, 7, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 45, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 45, 16, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 45, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 46, 48, 1] -8\n", - "[30, 92, 96, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 92, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 47, 50, 1] -8\n", - "[30, 94, 100, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 94, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 48, 15, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 48, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 49, 23, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 49, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 49, 42, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 49, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 50, 3, 0] -131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 50, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 51, 25, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (15, 51, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 51, 27, 1] -8\n", - "[30, 102, 54, 2] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 102, 54, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 1, 40, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 1, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 2, 26, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 2, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 3, 28, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 3, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 5, 39, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 5, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 7, 0, 1] 107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 7, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 8, 18, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 8, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 8, 23, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 8, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 9, 49, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 9, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 10, 16, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 10, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 11, 22, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 11, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 13, 4, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 13, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 13, 29, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 13, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 15, 22, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 15, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 16, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 16, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 16, 1, 1] -8\n", - "[32, 32, 2, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 32, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 17, 31, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 17, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 17, 41, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 17, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 18, 45, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 18, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 19, 38, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 19, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 20, 12, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 20, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 21, 17, 1] 4\n", - "[32, 42, 34, 2] 8\n", - "[48, 63, 51, 3] 4\n", - "[64, 84, 68, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (64, 84, 68, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 21, 44, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 21, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 22, 34, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 22, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 23, 45, 1] 8\n", - "[32, 46, 90, 2] -8\n", - "[48, 69, 135, 3] 8\n", - "[64, 92, 180, 4] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (64, 92, 180, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 180\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 77 * (103 - 77 )/103 =\n", - " = -103 + 154 * (26 )/103 =\n", - " = -103 + 154 * 26/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 25, 24, 1] 4\n", - "[32, 50, 48, 2] 4\n", - "[48, 75, 72, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 75, 72, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 25, 36, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 25, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 26, 3, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 26, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 26, 27, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 26, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 27, 24, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 27, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 28, 23, 1] 0\n", - "[32, 56, 46, 2] 4\n", - "[48, 84, 69, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 84, 69, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 28, 42, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 28, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 30, 51, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 30, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 33, 3, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 33, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 34, 30, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 34, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 37, 17, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 37, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 38, 40, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 38, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 38, 46, 1] -4\n", - "[32, 76, 92, 2] 4\n", - "[48, 114, 138, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 114, 138, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 138\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 39, 21, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 39, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 39, 37, 1] -4\n", - "[32, 78, 74, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 78, 74, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 42, 13, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 42, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 43, 7, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 43, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 44, 41, 1] -4\n", - "[32, 88, 82, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 88, 82, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 44, 49, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 44, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 45, 11, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 45, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 45, 15, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 45, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 46, 25, 1] -8\n", - "[32, 92, 50, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 92, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 47, 10, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 47, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 48, 20, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 48, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 48, 35, 1] -4\n", - "[32, 96, 70, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 96, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 50, 9, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 50, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 50, 44, 1] -8\n", - "[32, 100, 88, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 100, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 51, 39, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (16, 51, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 2, 5, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 2, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 3, 21, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 3, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 3, 37, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 3, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 4, 6, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 4, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 5, 47, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 5, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 6, 46, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 6, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 10, 11, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 10, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 10, 29, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 10, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 11, 48, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 11, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 12, 24, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 12, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 17, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 17, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 17, 1, 1] -8\n", - "[34, 34, 2, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 34, 2, 2)\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 18, 6, 1] -4\n", - "[34, 36, 12, 2] -8\n", - "[51, 54, 18, 3] -4\n", - "[68, 72, 24, 4] 8\n", - "[85, 90, 30, 5] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (85, 90, 30, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 85\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 85 * (103 - 85 )/103 =\n", - " = -103 + 170 * (18 )/103 =\n", - " = -103 + 170 * 18/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 19, 22, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 19, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 20, 3, 1] -8\n", - "[34, 40, 6, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 40, 6, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 20, 27, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 20, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 21, 7, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 21, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 21, 16, 1] 4\n", - "[34, 42, 32, 2] 4\n", - "[51, 63, 48, 3] 4\n", - "[68, 84, 64, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 84, 64, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 22, 14, 1] 0\n", - "[34, 44, 28, 2] 0\n", - "[51, 66, 42, 3] 8\n", - "[68, 88, 56, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 88, 56, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 22, 35, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 22, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 23, 31, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 23, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 24, 9, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 24, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 24, 44, 1] 8\n", - "[34, 48, 88, 2] -8\n", - "[51, 72, 132, 3] 8\n", - "[68, 96, 176, 4] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 96, 176, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 176\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 73 * (103 - 73 )/103 =\n", - " = -103 + 146 * (30 )/103 =\n", - " = -103 + 146 * 30/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 25, 50, 1] 8\n", - "[34, 50, 100, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 50, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 26, 39, 1] 8\n", - "[34, 52, 78, 2] 0\n", - "[51, 78, 117, 3] 4\n", - "[68, 104, 156, 4] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 104, 156, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 104\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 156\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 53 * (103 - 53 )/103 =\n", - " = -103 + 106 * (50 )/103 =\n", - " = -103 + 106 * 50/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 27, 21, 1] 0\n", - "[34, 54, 42, 2] 4\n", - "[51, 81, 63, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 81, 63, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 27, 50, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 27, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 28, 17, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 28, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 29, 48, 1] 4\n", - "[34, 58, 96, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 58, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 30, 32, 1] 4\n", - "[34, 60, 64, 2] 4\n", - "[51, 90, 96, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 90, 96, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 31, 40, 1] 4\n", - "[34, 62, 80, 2] 0\n", - "[51, 93, 120, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 93, 120, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 32, 18, 1] -4\n", - "[34, 64, 36, 2] 4\n", - "[51, 96, 54, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 96, 54, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 32, 23, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 32, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 33, 39, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 33, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 35, 3, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 35, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 36, 9, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 36, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 37, 16, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 37, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 38, 34, 1] 0\n", - "[34, 76, 68, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 76, 68, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 39, 10, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 39, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 40, 30, 1] -4\n", - "[34, 80, 60, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 80, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 42, 31, 1] -4\n", - "[34, 84, 62, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 84, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 42, 41, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 42, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 43, 4, 1] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 43, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 43, 18, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 43, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 44, 0, 1] 71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 44, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 46, 30, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 46, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 47, 13, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 47, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 48, 26, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 48, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 48, 33, 1] -4\n", - "[34, 96, 66, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 96, 66, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 49, 19, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 49, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 50, 7, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 50, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 51, 47, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (17, 51, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 2, 14, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 2, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 2, 35, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 2, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 3, 32, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 3, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 3, 43, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 3, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 4, 1, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 4, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 4, 38, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 4, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 7, 31, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 7, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 8, 7, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 8, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 8, 16, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 8, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 9, 13, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 9, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 11, 2, 1] 4\n", - "[36, 22, 4, 2] -4\n", - "[54, 33, 6, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 33, 6, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 12, 51, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 12, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 13, 19, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 13, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 14, 39, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 14, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 15, 2, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 15, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 16, 6, 1] 0\n", - "[36, 32, 12, 2] -4\n", - "[54, 48, 18, 3] -4\n", - "[72, 64, 24, 4] 4\n", - "[90, 80, 30, 5] 4\n", - "[108, 96, 36, 6] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (108, 96, 36, 6)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 4\n", - "Sigma = 9857/103 ~ 95\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 17, 45, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 17, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 18, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 18, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 18, 1, 1] -8\n", - "[36, 36, 2, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 36, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 19, 48, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 19, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 20, 30, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 20, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 21, 18, 1] 8\n", - "[36, 42, 36, 2] 4\n", - "[54, 63, 54, 3] 4\n", - "[72, 84, 72, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 84, 72, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 21, 23, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 21, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 22, 26, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 22, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 23, 0, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 23, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 24, 47, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 24, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 27, 32, 1] 8\n", - "[36, 54, 64, 2] 4\n", - "[54, 81, 96, 3] 0\n", - "[72, 108, 128, 4] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 108, 128, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 128\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 28, 7, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 28, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 29, 38, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 29, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 30, 24, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 30, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 31, 15, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 31, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 32, 17, 1] -4\n", - "[36, 64, 34, 2] 8\n", - "[54, 96, 51, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 96, 51, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 32, 44, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 32, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 34, 3, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 34, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 34, 27, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 34, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 36, 47, 1] 0\n", - "[36, 72, 94, 2] -4\n", - "[54, 108, 141, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 108, 141, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 37, 4, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 37, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 37, 18, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 37, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 38, 20, 1] -8\n", - "[36, 76, 40, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 76, 40, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 39, 8, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 39, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 40, 12, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 40, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 41, 11, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 41, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 41, 15, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 41, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 43, 17, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 43, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 44, 45, 1] -4\n", - "[36, 88, 90, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 88, 90, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 46, 12, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 46, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 47, 49, 1] -4\n", - "[36, 94, 98, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 94, 98, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 48, 34, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 48, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 49, 11, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 49, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 49, 29, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 49, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 50, 23, 1] -8\n", - "[36, 100, 46, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 100, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 50, 42, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (18, 50, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 0, 19, 1] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 0, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 1, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 1, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 2, 40, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 2, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 2, 46, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 2, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 3, 24, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 3, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 3, 36, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 3, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 4, 45, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 4, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 5, 30, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 5, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 7, 10, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 7, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 8, 42, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 8, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 9, 21, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 9, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 9, 37, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 9, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 10, 7, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 10, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 12, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 12, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 12, 35, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 12, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 13, 18, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 13, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 13, 23, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 13, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 14, 12, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 14, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 17, 49, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 17, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 18, 13, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 18, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 19, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 19, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 19, 1, 1] -8\n", - "[38, 38, 2, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 38, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 21, 9, 1] 0\n", - "[38, 42, 18, 2] 0\n", - "[57, 63, 27, 3] 4\n", - "[76, 84, 36, 4] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 84, 36, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 23, 13, 1] 0\n", - "[38, 46, 26, 2] 4\n", - "[57, 69, 39, 3] 8\n", - "[76, 92, 52, 4] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 92, 52, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 24, 3, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 24, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 25, 26, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 25, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 25, 33, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 25, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 26, 25, 1] 8\n", - "[38, 52, 50, 2] 4\n", - "[57, 78, 75, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (57, 78, 75, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 75\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 27, 33, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 27, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 27, 36, 1] 8\n", - "[38, 54, 72, 2] 4\n", - "[57, 81, 108, 3] -4\n", - "[76, 108, 144, 4] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 108, 144, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 29, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 29, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 30, 5, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 30, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[19, 32, 47, 1] 4\n", - "[38, 64, 94, 2] -8\n", - "[57, 96, 141, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (57, 96, 141, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 33, 25, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 33, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 33, 27, 1] 4\n", - "[38, 66, 54, 2] 8\n", - "[57, 99, 81, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (57, 99, 81, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 35, 12, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 35, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 36, 3, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 36, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 36, 27, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 36, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 37, 9, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 37, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 37, 44, 1] 0\n", - "[38, 74, 88, 2] 4\n", - "[57, 111, 132, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (57, 111, 132, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 132\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 39, 50, 1] 0\n", - "[38, 78, 100, 2] -4\n", - "[57, 117, 150, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (57, 117, 150, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 117\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 150\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 40, 2, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 40, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 42, 8, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 42, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 43, 47, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 43, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 44, 37, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 44, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 45, 4, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 45, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 45, 29, 1] -4\n", - "[38, 90, 58, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 90, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 46, 2, 0] -127\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 46, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 47, 32, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 47, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 47, 43, 1] 0\n", - "[38, 94, 86, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 94, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 49, 17, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 49, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 50, 39, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (19, 50, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 0, 42, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 0, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 1, 23, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 1, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 1, 42, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 1, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 2, 4, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 2, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 2, 29, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 2, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 4, 21, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 4, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 4, 50, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 4, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 5, 48, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 5, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 6, 7, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 6, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 7, 24, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 7, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 8, 30, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 8, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 9, 14, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 9, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 10, 3, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 10, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 11, 37, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 11, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 13, 39, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 13, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 14, 38, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 14, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 15, 49, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 15, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 16, 28, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 16, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 18, 50, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 18, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 19, 8, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 19, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 20, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 20, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 20, 1, 1] -8\n", - "[40, 40, 2, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 40, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 21, 12, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 21, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 23, 51, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 23, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 25, 15, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 25, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 28, 30, 1] 8\n", - "[40, 56, 60, 2] 8\n", - "[60, 84, 90, 3] 8\n", - "[80, 112, 120, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 112, 120, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 112\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 29, 21, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 29, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 29, 37, 1] 8\n", - "[40, 58, 74, 2] 4\n", - "[60, 87, 111, 3] 8\n", - "[80, 116, 148, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 116, 148, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 116\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 148\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 31, 47, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 31, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 32, 25, 1] 4\n", - "[40, 64, 50, 2] 8\n", - "[60, 96, 75, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 96, 75, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 75\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 33, 22, 1] 0\n", - "[40, 66, 44, 2] 8\n", - "[60, 99, 66, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 99, 66, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 34, 6, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 34, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 35, 1, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 35, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 35, 38, 1] 4\n", - "[40, 70, 76, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 70, 76, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 36, 22, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 36, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 38, 18, 1] -4\n", - "[40, 76, 36, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 76, 36, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 38, 23, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 38, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 39, 20, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 39, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 39, 35, 1] 4\n", - "[40, 78, 70, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 78, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 40, 45, 1] 0\n", - "[40, 80, 90, 2] 8\n", - "[60, 120, 135, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 120, 135, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 135\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 41, 47, 1] 0\n", - "[40, 82, 94, 2] 8\n", - "[60, 123, 141, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 123, 141, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 123\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 42, 5, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 42, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 42, 51, 1] 0\n", - "[40, 84, 102, 2] 0\n", - "[60, 126, 153, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 126, 153, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 126\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 153\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 43, 25, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 43, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 43, 27, 1] 0\n", - "[40, 86, 54, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 86, 54, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 45, 9, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 45, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 46, 45, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 46, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 47, 26, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 47, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 47, 33, 1] 0\n", - "[40, 94, 66, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 94, 66, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 48, 16, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 48, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 50, 12, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 50, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 51, 48, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (20, 51, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -8\n", - "Sigma = -8113/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 1, 30, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 1, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 2, 39, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 2, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 3, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 3, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 4, 20, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 4, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 5, 10, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 5, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 6, 25, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 6, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 6, 27, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 6, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 8, 6, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 8, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 9, 19, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 9, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 10, 22, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 10, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 11, 14, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 11, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 11, 35, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 11, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 12, 42, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 12, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 13, 48, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 13, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 14, 8, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 14, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 15, 14, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 15, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 17, 40, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 17, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 19, 34, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 19, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 20, 28, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 20, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 21, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 21, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 21, 1, 1] -8\n", - "[42, 42, 2, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 42, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 24, 41, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 24, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 24, 49, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 24, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 25, 9, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 25, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 25, 44, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 25, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 26, 21, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 26, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 26, 37, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 26, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 27, 17, 1] 4\n", - "[42, 54, 34, 2] 8\n", - "[63, 81, 51, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (63, 81, 51, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 81\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 27, 44, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 27, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 28, 31, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 28, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 29, 20, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 29, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 29, 35, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 29, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 32, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 32, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 33, 37, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 33, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 34, 32, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 34, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 34, 43, 1] 8\n", - "[42, 68, 86, 2] 4\n", - "[63, 102, 129, 3] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (63, 102, 129, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 35, 8, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 35, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 35, 28, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 35, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 36, 49, 1] 4\n", - "[42, 72, 98, 2] -8\n", - "[63, 108, 147, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (63, 108, 147, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 147\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 37, 1, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 37, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 37, 38, 1] 4\n", - "[42, 74, 76, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 74, 76, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 38, 30, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 38, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 39, 16, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 39, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 40, 51, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 40, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 41, 2, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 41, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 46, 50, 1] 0\n", - "[42, 92, 100, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 92, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 47, 11, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 47, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 47, 29, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 47, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 48, 3, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 48, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 49, 2, 1] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 49, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 50, 0, 1] 75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 50, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 51, 10, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (21, 51, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 0, 49, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 0, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 1, 41, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 1, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 1, 49, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 1, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 2, 6, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 2, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 3, 12, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 3, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 5, 46, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 5, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 6, 45, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 6, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 7, 9, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 7, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 9, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 9, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 10, 21, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 10, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 10, 50, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 10, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 11, 7, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 11, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 11, 16, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 11, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 12, 22, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 12, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 13, 32, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 13, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 13, 43, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 13, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 15, 16, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 15, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 16, 9, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 16, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 16, 44, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 16, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 18, 47, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 18, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 19, 17, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 19, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 20, 15, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 20, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 21, 24, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 21, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 21, 36, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 21, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 22, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 22, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 22, 1, 1] -8\n", - "[44, 44, 2, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 44, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 23, 47, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 23, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 24, 14, 1] 4\n", - "[44, 48, 28, 2] 0\n", - "[66, 72, 42, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 72, 42, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 24, 35, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 24, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 25, 48, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 25, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 29, 7, 1] -8\n", - "[44, 58, 14, 2] -8\n", - "[66, 87, 21, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 87, 21, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 30, 2, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 30, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 31, 13, 1] -4\n", - "[44, 62, 26, 2] 4\n", - "[66, 93, 39, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 93, 39, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 32, 5, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 32, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 32, 51, 1] 8\n", - "[44, 64, 102, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 64, 102, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 33, 20, 1] 0\n", - "[44, 66, 40, 2] 8\n", - "[66, 99, 60, 3] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 99, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 34, 40, 1] 8\n", - "[44, 68, 80, 2] 4\n", - "[66, 102, 120, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 102, 120, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 36, 20, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 36, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 36, 35, 1] 8\n", - "[44, 72, 70, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 72, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 37, 24, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 37, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 38, 31, 1] 4\n", - "[44, 76, 62, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 76, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 38, 41, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 38, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 39, 25, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 39, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 39, 27, 1] 4\n", - "[44, 78, 54, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 78, 54, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 41, 8, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 41, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 43, 51, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 43, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 45, 10, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 45, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 49, 8, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 49, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 49, 28, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 49, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 50, 33, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (22, 50, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 50, 36, 1] 0\n", - "[44, 100, 72, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 100, 72, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 51, 26, 1] 0\n", - "[44, 102, 52, 2] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 102, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 1, 20, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 1, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 2, 14, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 2, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 3, 43, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 3, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 4, 38, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 4, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 6, 34, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 6, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 7, 6, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 7, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 8, 16, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 8, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 9, 45, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 9, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 11, 2, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 11, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 12, 50, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 12, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 13, 19, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 13, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 14, 39, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 14, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 16, 6, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 16, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 18, 1, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 18, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 18, 38, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 18, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 19, 48, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 19, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 21, 4, 1] -4\n", - "[46, 42, 8, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 42, 8, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 21, 18, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 21, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 22, 26, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 22, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 22, 33, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 22, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 23, 0, 0] -8\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 23, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 23, 1, 1] -8\n", - "[46, 46, 2, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 46, 2, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 25, 32, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 25, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 27, 32, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 27, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 27, 43, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 27, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 28, 7, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 28, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 28, 16, 1] 4\n", - "[46, 56, 32, 2] 4\n", - "[69, 84, 48, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (69, 84, 48, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 29, 2, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 29, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 30, 28, 1] 8\n", - "[46, 60, 56, 2] 4\n", - "[69, 90, 84, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (69, 90, 84, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 32, 17, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 32, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 33, 47, 1] 8\n", - "[46, 66, 94, 2] -8\n", - "[69, 99, 141, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (69, 99, 141, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 34, 3, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 34, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 35, 39, 1] 8\n", - "[46, 70, 78, 2] 8\n", - "[69, 105, 117, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (69, 105, 117, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 117\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 36, 47, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 36, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 37, 4, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 37, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 37, 29, 1] 4\n", - "[46, 74, 58, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 74, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 38, 20, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 38, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 38, 35, 1] 8\n", - "[46, 76, 70, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 76, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 39, 13, 1] -8\n", - "[46, 78, 26, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 78, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 40, 12, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 40, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 41, 15, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 41, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 42, 0, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 42, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 44, 45, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 44, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 45, 40, 1] 4\n", - "[46, 90, 80, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 90, 80, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 47, 41, 1] 4\n", - "[46, 94, 82, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 94, 82, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 47, 49, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 47, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 48, 5, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 48, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 49, 11, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 49, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 49, 15, 1] -8\n", - "[46, 98, 30, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 98, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 50, 18, 1] -4\n", - "[46, 100, 36, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 100, 36, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 50, 23, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (23, 50, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 51, 42, 1] 4\n", - "[46, 102, 84, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 102, 84, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 2, 47, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 2, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 3, 19, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 3, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 4, 26, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 4, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 4, 33, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 4, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 5, 45, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 5, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 6, 39, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 6, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 7, 20, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 7, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 7, 35, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 7, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 8, 2, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 8, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 11, 24, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 11, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 11, 36, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 11, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 12, 17, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 12, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 14, 41, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 14, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 14, 49, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 14, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 15, 24, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 15, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 16, 14, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 16, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 16, 35, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 16, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 17, 34, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 17, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 18, 26, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 18, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 20, 37, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 20, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 21, 22, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 21, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 23, 46, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 23, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 24, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 24, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 24, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 25, 7, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 25, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 25, 16, 1] 4\n", - "[48, 50, 32, 2] 4\n", - "[72, 75, 48, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 75, 48, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 26, 10, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 26, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 27, 16, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 27, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 28, 38, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 28, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 29, 33, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 29, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 29, 36, 1] 8\n", - "[48, 58, 72, 2] 4\n", - "[72, 87, 108, 3] 4\n", - "[96, 116, 144, 4] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 116, 144, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 116\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 30, 4, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 30, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 30, 18, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 30, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 31, 30, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 31, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 32, 6, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 32, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 34, 13, 1] -8\n", - "[48, 68, 26, 2] 8\n", - "[72, 102, 39, 3] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 102, 39, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 35, 49, 1] 4\n", - "[48, 70, 98, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 70, 98, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 36, 0, 1] 79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 36, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 37, 22, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 37, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 39, 11, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 39, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 39, 15, 1] -8\n", - "[48, 78, 30, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 78, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 40, 32, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 40, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 40, 43, 1] 4\n", - "[48, 80, 86, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 80, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 41, 30, 1] 0\n", - "[48, 82, 60, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 82, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 42, 40, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 42, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 42, 46, 1] 0\n", - "[48, 84, 92, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 84, 92, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 43, 48, 1] 0\n", - "[48, 86, 96, 2] 8\n", - "[72, 129, 144, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 129, 144, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 129\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 45, 25, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 45, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 45, 27, 1] 0\n", - "[48, 90, 54, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 90, 54, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 46, 43, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 46, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 48, 9, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 48, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 51, 45, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (24, 51, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 0, 32, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 0, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 1, 32, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 1, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 1, 43, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 1, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 2, 10, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 2, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 3, 38, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 3, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 4, 3, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 4, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 5, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 5, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 5, 15, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 5, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 6, 21, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 6, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 6, 37, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 6, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 8, 26, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 8, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 10, 14, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 10, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 12, 31, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 12, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 13, 33, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 13, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 13, 36, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 13, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 15, 42, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 15, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 17, 30, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 17, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 18, 3, 1] 0\n", - "[50, 36, 6, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 36, 6, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 18, 27, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 18, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 19, 47, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 19, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 21, 34, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 21, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 22, 13, 1] 4\n", - "[50, 44, 26, 2] 4\n", - "[75, 66, 39, 3] 4\n", - "[100, 88, 52, 4] 4\n", - "[125, 110, 65, 5] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (125, 110, 65, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 125\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 110\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 65\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 65 * (103 - 65 )/103 =\n", - " = -103 + 130 * (38 )/103 =\n", - " = -103 + 130 * 38/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 23, 25, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 23, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 23, 27, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 23, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 24, 40, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 24, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 25, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 25, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 25, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 25, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 26, 19, 1] 8\n", - "[50, 52, 38, 2] 4\n", - "[75, 78, 57, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (75, 78, 57, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 75\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 27, 1, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 27, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 27, 38, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 27, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 28, 46, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 28, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 31, 50, 1] 8\n", - "[50, 62, 100, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 62, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 32, 20, 1] 0\n", - "[50, 64, 40, 2] 8\n", - "[75, 96, 60, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (75, 96, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 75\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 33, 19, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 33, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 34, 4, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 34, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 34, 29, 1] 4\n", - "[50, 68, 58, 2] 8\n", - "[75, 102, 87, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (75, 102, 87, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 75\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 37, 34, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 37, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 38, 43, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 38, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 39, 22, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 39, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 40, 7, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 40, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 41, 51, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 41, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 42, 25, 1] 0\n", - "[50, 84, 50, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 84, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 43, 20, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 43, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 43, 35, 1] 4\n", - "[50, 86, 70, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 86, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 44, 30, 1] 0\n", - "[50, 88, 60, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 88, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 45, 24, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 45, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 46, 7, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 46, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 46, 16, 1] -8\n", - "[50, 92, 32, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 92, 32, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 48, 49, 1] 0\n", - "[50, 96, 98, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 96, 98, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 49, 5, 0] -123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 49, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 49, 51, 1] 0\n", - "[50, 98, 102, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 98, 102, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 51, 15, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (25, 51, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 0, 47, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 0, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 1, 47, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 1, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 2, 7, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 2, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 2, 16, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 2, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 3, 40, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 3, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 4, 24, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 4, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 6, 9, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 6, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 6, 44, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 6, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 8, 25, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 8, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 9, 34, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 9, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 11, 8, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 11, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 11, 28, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 11, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 13, 3, 1] 8\n", - "[52, 26, 6, 2] -4\n", - "[78, 39, 9, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 39, 9, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 13, 27, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 13, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 14, 6, 1] 8\n", - "[52, 28, 12, 2] 0\n", - "[78, 42, 18, 3] -8\n", - "[104, 56, 24, 4] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (104, 56, 24, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 104\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 15, 8, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 15, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 17, 5, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 17, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 17, 51, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 17, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 18, 24, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 18, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 18, 36, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 18, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 19, 32, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 19, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 19, 43, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 19, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 20, 31, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 20, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 20, 41, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 20, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 22, 18, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 22, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 22, 23, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 22, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 23, 33, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 23, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 23, 36, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 23, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 24, 2, 1] -8\n", - "[52, 48, 4, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 48, 4, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 25, 19, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 25, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 26, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 26, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 26, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 26, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 29, 28, 1] 8\n", - "[52, 58, 56, 2] 4\n", - "[78, 87, 84, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 87, 84, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 30, 11, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 30, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 30, 15, 1] 0\n", - "[52, 60, 30, 2] 4\n", - "[78, 90, 45, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 90, 45, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 31, 39, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 31, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 33, 1, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 33, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 33, 38, 1] 8\n", - "[52, 66, 76, 2] 8\n", - "[78, 99, 114, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 99, 114, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 114\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 34, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 34, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 35, 31, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 35, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 36, 38, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 36, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 37, 30, 1] 4\n", - "[52, 74, 60, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 74, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 40, 10, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 40, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 41, 39, 1] 4\n", - "[52, 82, 78, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 82, 78, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 42, 26, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 42, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 42, 33, 1] 4\n", - "[52, 84, 66, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 84, 66, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 43, 12, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 43, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 44, 5, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 44, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 47, 20, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 47, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 47, 35, 1] 4\n", - "[52, 94, 70, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 94, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 48, 17, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (26, 48, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 51, 22, 1] -4\n", - "[52, 102, 44, 2] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (52, 102, 44, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 1, 32, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 1, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 2, 10, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 2, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 3, 1, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 3, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 3, 38, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 3, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 4, 3, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 4, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 4, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 4, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 5, 11, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 5, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 5, 29, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 5, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 6, 21, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 6, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 6, 50, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 6, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 7, 12, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 7, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 8, 46, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 8, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 10, 14, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 10, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 10, 35, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 10, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 12, 31, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 12, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 12, 41, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 12, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 13, 26, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 13, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 13, 33, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 13, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 17, 30, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 17, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 18, 25, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 18, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 18, 27, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 18, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 20, 17, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 20, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 22, 8, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 22, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 23, 25, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 23, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 25, 0, 1] 91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 25, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 26, 16, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 26, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 27, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 27, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 27, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 27, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 28, 40, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 28, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 28, 46, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 28, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 29, 3, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 29, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[27, 30, 45, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 30, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 31, 51, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 31, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 33, 19, 1] 4\n", - "[54, 66, 38, 2] 8\n", - "[81, 99, 57, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (81, 99, 57, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 34, 4, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 34, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 34, 18, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 34, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 36, 19, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 36, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 37, 34, 1] 8\n", - "[54, 74, 68, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 74, 68, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 38, 32, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 38, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 38, 43, 1] 8\n", - "[54, 76, 86, 2] 8\n", - "[81, 114, 129, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (81, 114, 129, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 39, 22, 1] 0\n", - "[54, 78, 44, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 78, 44, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 41, 5, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 41, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 41, 51, 1] 4\n", - "[54, 82, 102, 2] -4\n", - "[81, 123, 153, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (81, 123, 153, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -8\n", - "Sigma = -7869/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 123\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 153\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 43, 20, 1] -4\n", - "[54, 86, 40, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 86, 40, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 45, 24, 1] 0\n", - "[54, 90, 48, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 90, 48, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 45, 36, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 45, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 46, 7, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 46, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 47, 48, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 47, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 48, 37, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 48, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 49, 5, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 49, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 51, 11, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (27, 51, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 51, 15, 1] -8\n", - "[54, 102, 30, 2] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (54, 102, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 0, 12, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 0, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 1, 12, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 1, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 3, 7, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 3, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 3, 16, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 3, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 4, 46, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 4, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 5, 13, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 5, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 6, 30, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 6, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 8, 1, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 8, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 8, 38, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 8, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 9, 11, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 9, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 9, 15, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 9, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 10, 48, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 10, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 11, 26, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 11, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 11, 33, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 11, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 12, 9, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 12, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 12, 44, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 12, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 13, 2, 1] 8\n", - "[56, 26, 4, 2] -8\n", - "[84, 39, 6, 3] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 39, 6, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 14, 37, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 14, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 15, 33, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 15, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 15, 36, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 15, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 16, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 16, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 18, 40, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 18, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 18, 46, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 18, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 19, 14, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 19, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 19, 35, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 19, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 20, 21, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 20, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 20, 50, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 20, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 22, 3, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 22, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 23, 40, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 23, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 26, 43, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 26, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 27, 7, 1] -4\n", - "[56, 54, 14, 2] -8\n", - "[84, 81, 21, 3] 4\n", - "[112, 108, 28, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (112, 108, 28, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 112\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 28, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 28, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 28, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 28, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 29, 26, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 29, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 30, 23, 1] 8\n", - "[56, 60, 46, 2] 4\n", - "[84, 90, 69, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 90, 69, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 30, 42, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 30, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 32, 31, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 32, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 33, 10, 1] -4\n", - "[56, 66, 20, 2] 0\n", - "[84, 99, 30, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 99, 30, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 34, 8, 1] -8\n", - "[56, 68, 16, 2] 0\n", - "[84, 102, 24, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 102, 24, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 34, 28, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 34, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 35, 21, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 35, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 35, 37, 1] 8\n", - "[56, 70, 74, 2] 8\n", - "[84, 105, 111, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 105, 111, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 111\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 36, 10, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 36, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 39, 4, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 39, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 39, 29, 1] 4\n", - "[56, 78, 58, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (56, 78, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 43, 6, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 43, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 44, 15, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 44, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 46, 32, 1] 4\n", - "[56, 92, 64, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (56, 92, 64, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 48, 39, 1] 4\n", - "[56, 96, 78, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (56, 96, 78, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 49, 22, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 49, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 50, 45, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 50, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 51, 13, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (28, 51, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -12\n", - "Sigma = -7645/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 2, 20, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 2, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 4, 0, 1] 123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 4, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 5, 3, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 5, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 5, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 5, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 6, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 6, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 7, 41, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 7, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 7, 49, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 7, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 9, 8, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 9, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 10, 17, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 10, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 11, 1, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 11, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 11, 38, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 11, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 12, 5, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 12, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 13, 7, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 13, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 13, 16, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 13, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 14, 30, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 14, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 15, 38, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 15, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 16, 31, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 16, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 16, 41, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 16, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 17, 13, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 17, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 19, 6, 1] 4\n", - "[58, 38, 12, 2] -8\n", - "[87, 57, 18, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (87, 57, 18, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 57\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 21, 42, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 21, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 22, 40, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 22, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 22, 46, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 22, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 23, 10, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 23, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 25, 14, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 25, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 26, 12, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 26, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 28, 47, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 28, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 29, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 29, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 29, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 29, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 30, 33, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 30, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 30, 36, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 30, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 31, 11, 1] 0\n", - "[58, 62, 22, 2] 0\n", - "[87, 93, 33, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (87, 93, 33, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 31, 29, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 31, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 32, 9, 1] -4\n", - "[58, 64, 18, 2] 0\n", - "[87, 96, 27, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (87, 96, 27, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 34, 25, 1] 8\n", - "[58, 68, 50, 2] 8\n", - "[87, 102, 75, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (87, 102, 75, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 75\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 35, 30, 1] 8\n", - "[58, 70, 60, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 70, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 37, 23, 1] 4\n", - "[58, 74, 46, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 74, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 37, 42, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 37, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 39, 28, 1] 4\n", - "[58, 78, 56, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 78, 56, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 40, 48, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 40, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 41, 4, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 41, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 41, 29, 1] 4\n", - "[58, 82, 58, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 82, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 42, 10, 1] -8\n", - "[58, 84, 20, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 84, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 43, 9, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 43, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 43, 44, 1] 4\n", - "[58, 86, 88, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 86, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 44, 13, 1] -8\n", - "[58, 88, 26, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 88, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 45, 19, 1] 0\n", - "[58, 90, 38, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 90, 38, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 47, 21, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 47, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 47, 37, 1] 4\n", - "[58, 94, 74, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (58, 94, 74, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 49, 4, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 49, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 49, 18, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 49, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 51, 3, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (29, 51, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 0, 50, 1] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 0, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 1, 21, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 1, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 1, 50, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 1, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 2, 49, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 2, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 3, 6, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 3, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 5, 19, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 5, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 6, 8, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 6, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 6, 28, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 6, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 7, 30, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 7, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 8, 20, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 8, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 8, 35, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 8, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 10, 5, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 10, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 11, 47, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 11, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 12, 45, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 12, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 13, 14, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 13, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 14, 11, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 14, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 14, 29, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 14, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 15, 47, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 15, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 17, 25, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 17, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 17, 27, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 17, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 19, 39, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 19, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 20, 4, 1] 0\n", - "[60, 40, 8, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 40, 8, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 20, 18, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 20, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 21, 46, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 21, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 22, 10, 1] 8\n", - "[60, 44, 20, 2] -4\n", - "[90, 66, 30, 3] -8\n", - "[120, 88, 40, 4] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (120, 88, 40, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 23, 12, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 23, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 25, 31, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 25, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 27, 6, 1] -4\n", - "[60, 54, 12, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 54, 12, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 28, 20, 1] 8\n", - "[60, 56, 40, 2] 4\n", - "[90, 84, 60, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 84, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 30, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 30, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 30, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 30, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 31, 24, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 31, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 34, 16, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 34, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 35, 4, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 35, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 35, 29, 1] 8\n", - "[60, 70, 58, 2] 8\n", - "[90, 105, 87, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 105, 87, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 87\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 37, 26, 1] 8\n", - "[60, 74, 52, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 74, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 38, 21, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 38, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 38, 37, 1] 8\n", - "[60, 76, 74, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 76, 74, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 39, 2, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 39, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 40, 17, 1] 0\n", - "[60, 80, 34, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 80, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 40, 44, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 40, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 41, 24, 1] 4\n", - "[60, 82, 48, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 82, 48, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 41, 36, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 41, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 42, 12, 1] -8\n", - "[60, 84, 24, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 84, 24, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 43, 34, 1] 8\n", - "[60, 86, 68, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 86, 68, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 44, 25, 1] 4\n", - "[60, 88, 50, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 88, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 46, 17, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 46, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 48, 13, 1] -8\n", - "[60, 96, 26, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 96, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 49, 33, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 49, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 49, 36, 1] 4\n", - "[60, 98, 72, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 98, 72, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 50, 40, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (30, 50, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -12\n", - "Sigma = -7465/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 50, 46, 1] 4\n", - "[60, 100, 92, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (60, 100, 92, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 3, 39, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 3, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 6, 38, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 6, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 7, 4, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 7, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 7, 18, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 7, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 8, 37, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 8, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 10, 13, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 10, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 12, 25, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 12, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 12, 27, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 12, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 13, 41, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 13, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 13, 49, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 13, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 14, 33, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 14, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 14, 36, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 14, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 16, 4, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 16, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 16, 29, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 16, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 17, 7, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 17, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 17, 16, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 17, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 19, 11, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 19, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 19, 15, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 19, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 20, 26, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 20, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 21, 43, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 21, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 22, 48, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 22, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 23, 17, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 23, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 24, 50, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 24, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 25, 30, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 25, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 26, 5, 1] -4\n", - "[62, 52, 10, 2] -8\n", - "[93, 78, 15, 3] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (93, 78, 15, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 28, 21, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 28, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 28, 37, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 28, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 31, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 31, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 31, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 31, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 32, 8, 1] -4\n", - "[62, 64, 16, 2] 0\n", - "[93, 96, 24, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (93, 96, 24, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 32, 28, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 32, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 33, 5, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 33, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 33, 51, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 33, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 34, 14, 1] 0\n", - "[62, 68, 28, 2] 8\n", - "[93, 102, 42, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (93, 102, 42, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 34, 35, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 34, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 35, 26, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 35, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 35, 33, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 35, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 36, 51, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 36, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 37, 10, 1] -4\n", - "[62, 74, 20, 2] 8\n", - "[93, 111, 30, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (93, 111, 30, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 38, 22, 1] 4\n", - "[62, 76, 44, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (62, 76, 44, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 39, 47, 1] 8\n", - "[62, 78, 94, 2] 4\n", - "[93, 117, 141, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (93, 117, 141, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 117\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 41, 0, 1] 83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 41, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 42, 17, 1] 0\n", - "[62, 84, 34, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (62, 84, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 42, 44, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 42, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 43, 8, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 43, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 44, 7, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 44, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 45, 31, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 45, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 46, 34, 1] 8\n", - "[62, 92, 68, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (62, 92, 68, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 47, 42, 1] 8\n", - "[62, 94, 84, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (62, 94, 84, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 48, 2, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 48, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 50, 32, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (31, 50, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 50, 43, 1] 8\n", - "[62, 100, 86, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (62, 100, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 0, 25, 1] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 0, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 1, 25, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 1, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 1, 27, 1] 56\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 1, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 3, 4, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 3, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 3, 18, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 3, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 4, 34, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 4, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 5, 49, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 5, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 7, 40, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 7, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 7, 46, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 7, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 10, 2, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 10, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 11, 5, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 11, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 13, 22, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 13, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 14, 10, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 14, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 15, 5, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 15, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 15, 51, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 15, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 16, 46, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 16, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 19, 26, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 19, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 19, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 19, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 20, 32, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 20, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 20, 43, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 20, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 21, 6, 1] 4\n", - "[64, 42, 12, 2] -8\n", - "[96, 63, 18, 3] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 63, 18, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 63\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 22, 39, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 22, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 24, 45, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 24, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 25, 23, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 25, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 25, 42, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 25, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 26, 8, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 26, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 27, 18, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 27, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 27, 23, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 27, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 29, 34, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 29, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 30, 17, 1] 8\n", - "[64, 60, 34, 2] 8\n", - "[96, 90, 51, 3] 8\n", - "[128, 120, 68, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (128, 120, 68, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 128\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 30, 44, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 30, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 31, 12, 1] 0\n", - "[64, 62, 24, 2] 4\n", - "[96, 93, 36, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 93, 36, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 32, 0, 0] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 32, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 32, 1, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 32, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 33, 13, 1] 0\n", - "[64, 66, 26, 2] 8\n", - "[96, 99, 39, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 99, 39, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 99\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 34, 21, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 34, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 34, 37, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 34, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 35, 43, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 35, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 36, 13, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 36, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 37, 6, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 37, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 38, 3, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 38, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 38, 27, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 38, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 40, 24, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 40, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 42, 15, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 42, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 43, 1, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 43, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 43, 38, 1] 8\n", - "[64, 86, 76, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (64, 86, 76, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 46, 28, 1] 4\n", - "[64, 92, 56, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (64, 92, 56, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 47, 19, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 47, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 49, 48, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 49, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 50, 31, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 50, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 51, 41, 1] 8\n", - "[64, 102, 82, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (64, 102, 82, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 51, 49, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (32, 51, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 1, 47, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 1, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 2, 7, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 2, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 4, 24, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 4, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 4, 36, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 4, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 6, 9, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 6, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 7, 14, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 7, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 9, 34, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 9, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 10, 12, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 10, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 11, 28, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 11, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 13, 25, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 13, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 13, 27, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 13, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 14, 31, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 14, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 15, 8, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 15, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 15, 28, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 15, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 17, 5, 1] 4\n", - "[66, 34, 10, 2] -4\n", - "[99, 51, 15, 3] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (99, 51, 15, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 99\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 18, 33, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 18, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 18, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 18, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 19, 32, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 19, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 20, 41, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 20, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 20, 49, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 20, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 22, 23, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 22, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 22, 42, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 22, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 23, 26, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 23, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 23, 33, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 23, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 24, 38, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 24, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 25, 19, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 25, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 26, 0, 1] 91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 26, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 27, 19, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 27, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 28, 2, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 28, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 29, 24, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 29, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 30, 11, 1] 0\n", - "[66, 60, 22, 2] 0\n", - "[99, 90, 33, 3] 8\n", - "[132, 120, 44, 4] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (132, 120, 44, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 132\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 30, 29, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 30, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 31, 39, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 31, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 32, 48, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 32, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 33, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 33, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 33, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 33, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 34, 45, 1] 8\n", - "[66, 68, 90, 2] -4\n", - "[99, 102, 135, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (99, 102, 135, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 99\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 99 * (103 - 99 )/103 =\n", - " = -103 + 198 * (4 )/103 =\n", - " = -103 + 198 * 4/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 135\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 35, 31, 1] 8\n", - "[66, 70, 62, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 70, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 35, 41, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 35, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 36, 1, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 36, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 36, 38, 1] 8\n", - "[66, 72, 76, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 72, 76, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 38, 47, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 38, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 40, 10, 1] -8\n", - "[66, 80, 20, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 80, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 42, 26, 1] 4\n", - "[66, 84, 52, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 84, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 44, 34, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 44, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 45, 3, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 45, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 46, 10, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 46, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 47, 20, 1] -4\n", - "[66, 94, 40, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 94, 40, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 48, 17, 1] -4\n", - "[66, 96, 34, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (66, 96, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 48, 44, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 48, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 49, 30, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 49, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 50, 22, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (33, 50, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 0, 9, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 0, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 1, 9, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 1, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 1, 44, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 1, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 4, 32, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 4, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 5, 38, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 5, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 6, 23, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 6, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 6, 42, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 6, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 7, 51, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 7, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 8, 12, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 8, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 9, 26, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 9, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 9, 33, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 9, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 11, 43, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 11, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 12, 11, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 12, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 12, 15, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 12, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 15, 10, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 15, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 16, 50, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 16, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 17, 24, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 17, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 17, 36, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 17, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 19, 21, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 19, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 19, 37, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 19, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 20, 45, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 20, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 21, 25, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 21, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 22, 7, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 22, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 22, 16, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 22, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 24, 48, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 24, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 26, 6, 1] -4\n", - "[68, 52, 12, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 52, 12, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 28, 12, 1] 0\n", - "[68, 56, 24, 2] 0\n", - "[102, 84, 36, 3] -8\n", - "[136, 112, 48, 4] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (136, 112, 48, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 136\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 112\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 29, 32, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 29, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 29, 43, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 29, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 33, 6, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 33, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 34, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 34, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 34, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 34, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 36, 48, 1] 8\n", - "[68, 72, 96, 2] -8\n", - "[102, 108, 144, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 108, 144, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 37, 25, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 37, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 37, 27, 1] 8\n", - "[68, 74, 54, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 74, 54, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 38, 17, 1] 0\n", - "[68, 76, 34, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 76, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 38, 44, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 38, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 39, 46, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 39, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 40, 41, 1] 8\n", - "[68, 80, 82, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 80, 82, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 40, 49, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 40, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 42, 14, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 42, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 43, 30, 1] 4\n", - "[68, 86, 60, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 86, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 44, 33, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 44, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 44, 36, 1] 4\n", - "[68, 88, 72, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 88, 72, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 45, 47, 1] 4\n", - "[68, 90, 94, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 90, 94, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 46, 31, 1] 4\n", - "[68, 92, 62, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (68, 92, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 46, 41, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 46, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 47, 34, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 47, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 48, 4, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 48, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 48, 18, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 48, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 49, 3, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 49, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 51, 2, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (34, 51, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 1, 42, 1] 56\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 1, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 2, 4, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 2, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 2, 18, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 2, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 4, 50, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 4, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 5, 6, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 5, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 7, 24, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 7, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 7, 36, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 7, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 8, 30, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 8, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 9, 14, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 9, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 9, 35, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 9, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 10, 3, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 10, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 10, 27, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 10, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 11, 21, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 11, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 11, 37, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 11, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 12, 19, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 12, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 14, 1, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 14, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 14, 38, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 14, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 15, 37, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 15, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 16, 24, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 16, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 18, 51, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 18, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 19, 8, 1] 8\n", - "[70, 38, 16, 2] -4\n", - "[105, 57, 24, 3] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (105, 57, 24, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 57\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 19, 28, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 19, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 20, 0, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 20, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 21, 12, 1] 8\n", - "[70, 42, 24, 2] 0\n", - "[105, 63, 36, 3] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (105, 63, 36, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 63\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 22, 17, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 22, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 23, 5, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 23, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 23, 51, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 23, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 24, 22, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 24, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 25, 11, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 25, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 25, 15, 1] 8\n", - "[70, 50, 30, 2] 0\n", - "[105, 75, 45, 3] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (105, 75, 45, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 75\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 75 * (103 - 75 )/103 =\n", - " = -103 + 150 * (28 )/103 =\n", - " = -103 + 150 * 28/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 27, 15, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 27, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 29, 21, 1] 8\n", - "[70, 58, 42, 2] 4\n", - "[105, 87, 63, 3] 0\n", - "[140, 116, 84, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (140, 116, 84, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 140\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 116\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 29, 50, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 29, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 31, 47, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 31, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 34, 31, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 34, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 35, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 35, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 35, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 35, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 36, 22, 1] 4\n", - "[70, 72, 44, 2] 8\n", - "[105, 108, 66, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (105, 108, 66, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 105\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 37, 12, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 37, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 38, 23, 1] 4\n", - "[70, 76, 46, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 76, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 38, 42, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 38, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 39, 20, 1] 0\n", - "[70, 78, 40, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 78, 40, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 40, 13, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 40, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 42, 5, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 42, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 43, 25, 1] 4\n", - "[70, 86, 50, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 86, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 44, 14, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 44, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 45, 39, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 45, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 46, 45, 1] 4\n", - "[70, 92, 90, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 92, 90, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 47, 26, 1] 4\n", - "[70, 94, 52, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 94, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 48, 7, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (35, 48, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 48, 16, 1] -4\n", - "[70, 96, 32, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 96, 32, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 51, 48, 1] 4\n", - "[70, 102, 96, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (70, 102, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 3, 19, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 3, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 4, 33, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 4, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 4, 36, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 4, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 5, 45, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 5, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 6, 39, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 6, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 7, 14, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 7, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 7, 35, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 7, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 8, 2, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 8, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 10, 12, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 10, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 11, 24, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 11, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 13, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 13, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 14, 31, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 14, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 14, 41, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 14, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 15, 28, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 15, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 16, 14, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 16, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 17, 34, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 17, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 18, 26, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 18, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 18, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 18, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 20, 49, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 20, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 21, 22, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 21, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 22, 42, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 22, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 23, 26, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 23, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 24, 1, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 24, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 24, 38, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 24, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 25, 16, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 25, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 27, 19, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 27, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 28, 2, 1] -8\n", - "[72, 56, 4, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 56, 4, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 29, 24, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 29, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 29, 36, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 29, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 30, 4, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 30, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 30, 29, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 30, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 32, 48, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 32, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 33, 0, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 33, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 34, 13, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 34, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 35, 41, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 35, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 35, 49, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 35, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 36, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 36, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 36, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 36, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 38, 47, 1] 8\n", - "[72, 76, 94, 2] 0\n", - "[108, 114, 141, 3] 8\n", - "[144, 152, 188, 4] 0\n", - "[180, 190, 235, 5] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (180, 190, 235, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 180\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 77 * (103 - 77 )/103 =\n", - " = -103 + 154 * (26 )/103 =\n", - " = -103 + 154 * 26/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 190\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 235\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 39, 15, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 39, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 40, 43, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 40, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 41, 30, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 41, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 42, 46, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 42, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 43, 48, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 43, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 44, 34, 1] 8\n", - "[72, 88, 68, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 88, 68, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 45, 3, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 45, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 45, 27, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 45, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 46, 10, 1] -8\n", - "[72, 92, 20, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 92, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 48, 9, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (36, 48, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7433/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 48, 44, 1] 4\n", - "[72, 96, 88, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 96, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 49, 30, 1] 4\n", - "[72, 98, 60, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 98, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 50, 22, 1] 0\n", - "[72, 100, 44, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (72, 100, 44, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -12\n", - "Sigma = -7381/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 3, 17, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 3, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 3, 44, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 3, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 5, 43, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 5, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 6, 25, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 6, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 7, 15, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 7, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 8, 31, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 8, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 9, 19, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 9, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 11, 20, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 11, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 11, 35, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 11, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 13, 6, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 13, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 14, 8, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 14, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 14, 28, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 14, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 15, 14, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 15, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 15, 35, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 15, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 19, 34, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 19, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 20, 24, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 20, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 21, 0, 1] 99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 21, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 24, 49, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 24, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 25, 9, 1] 4\n", - "[74, 50, 18, 2] -4\n", - "[111, 75, 27, 3] -8\n", - "[148, 100, 36, 4] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (148, 100, 36, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 148\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 26, 21, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 26, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 26, 50, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 26, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 27, 9, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 27, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 27, 44, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 27, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 28, 31, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 28, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 28, 41, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 28, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 29, 20, 1] 8\n", - "[74, 58, 40, 2] 4\n", - "[111, 87, 60, 3] 8\n", - "[148, 116, 80, 4] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (148, 116, 80, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 148\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 116\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 30, 47, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 30, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 31, 2, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 31, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 32, 45, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 32, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 33, 21, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 33, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 33, 37, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 33, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 34, 32, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 34, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 35, 28, 1] 8\n", - "[74, 70, 56, 2] 8\n", - "[111, 105, 84, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (111, 105, 84, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 111\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 36, 37, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 36, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 37, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 37, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 37, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 37, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 38, 30, 1] 8\n", - "[74, 76, 60, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (74, 76, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 39, 7, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 39, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 39, 16, 1] 0\n", - "[74, 78, 32, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (74, 78, 32, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 78\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 40, 5, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 40, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 40, 51, 1] 8\n", - "[74, 80, 102, 2] -8\n", - "[111, 120, 153, 3] 4\n", - "[148, 160, 204, 4] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (148, 160, 204, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 148\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 160\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 204\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 101 * (103 - 101 )/103 =\n", - " = -103 + 202 * (2 )/103 =\n", - " = -103 + 202 * 2/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 41, 2, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 41, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 43, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 43, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 44, 19, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 44, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 45, 48, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 45, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 46, 51, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 46, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 47, 4, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 47, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 47, 29, 1] 4\n", - "[74, 94, 58, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (74, 94, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 48, 3, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 48, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 48, 27, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 48, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 49, 38, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (37, 49, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7373/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 51, 10, 1] -8\n", - "[74, 102, 20, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (74, 102, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 1, 0, 1] 131\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 1, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 2, 38, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 2, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 3, 25, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 3, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 3, 27, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 3, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 4, 18, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 4, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 4, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 4, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 5, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 5, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 6, 31, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 6, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 8, 28, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 8, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 9, 39, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 9, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 10, 43, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 10, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 11, 4, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 11, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 11, 29, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 11, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 13, 8, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 13, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 14, 20, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 14, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 14, 35, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 14, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 15, 11, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 15, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 15, 29, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 15, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 16, 7, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 16, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 17, 9, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 17, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 17, 44, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 17, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 18, 23, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 18, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 18, 42, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 18, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 19, 16, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 19, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 21, 50, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 21, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 23, 42, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 23, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 24, 33, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 24, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 24, 36, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 24, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 26, 46, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 26, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 27, 25, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 27, 25, 1)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 28, 24, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 28, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 29, 4, 1] -8\n", - "[76, 58, 8, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 58, 8, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 29, 18, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 29, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 31, 41, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 31, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 31, 49, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 31, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 33, 26, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 33, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 35, 20, 1] 4\n", - "[76, 70, 40, 2] 8\n", - "[114, 105, 60, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (114, 105, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 114\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 36, 26, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 36, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 36, 33, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 36, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 37, 21, 1] 4\n", - "[76, 74, 42, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 74, 42, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 74\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 37, 50, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 37, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 38, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 38, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 38, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 38, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 41, 49, 1] 8\n", - "[76, 82, 98, 2] -4\n", - "[114, 123, 147, 3] 4\n", - "[152, 164, 196, 4] -8\n", - "[190, 205, 245, 5] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (190, 205, 245, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 190\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "2. -T(2, 103), theta = 205\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 245\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 43, 32, 1] 8\n", - "[76, 86, 64, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 86, 64, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 44, 9, 1] -8\n", - "[76, 88, 18, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 88, 18, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 45, 13, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 45, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 46, 40, 1] 8\n", - "[76, 92, 80, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (76, 92, 80, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 48, 6, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 48, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 49, 37, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 49, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 50, 51, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 50, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 51, 5, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (38, 51, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 0, 5, 1] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 0, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 1, 5, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 1, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 1, 51, 1] 56\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 1, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 2, 21, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 2, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 2, 50, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 2, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 3, 31, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 3, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 3, 41, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 3, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 4, 12, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 4, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 5, 7, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 5, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 5, 16, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 5, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 6, 24, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 6, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 6, 36, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 6, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 9, 38, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 9, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 12, 13, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 12, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 13, 20, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 13, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 14, 18, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 14, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 14, 23, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 14, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 17, 2, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 17, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 19, 30, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 19, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 20, 42, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 20, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 22, 32, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 22, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 23, 48, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 23, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 25, 49, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 25, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 26, 17, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 26, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 26, 44, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 26, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 27, 41, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 27, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 27, 49, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 27, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 29, 12, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 29, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 30, 10, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 30, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 31, 26, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 31, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 31, 33, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 31, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 32, 11, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 32, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 32, 15, 1] 4\n", - "[78, 64, 30, 2] 0\n", - "[117, 96, 45, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (117, 96, 45, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 117\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 33, 17, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 33, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 35, 23, 1] 8\n", - "[78, 70, 46, 2] 4\n", - "[117, 105, 69, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (117, 105, 69, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 117\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -4\n", - "Sigma = -8529/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 105\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 69\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 69 * (103 - 69 )/103 =\n", - " = -103 + 138 * (34 )/103 =\n", - " = -103 + 138 * 34/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 35, 42, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 35, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 37, 40, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 37, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 38, 51, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 38, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 39, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 39, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 39, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 39, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 40, 39, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 40, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 41, 26, 1] 8\n", - "[78, 82, 52, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 82, 52, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 82\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 52\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 42, 48, 1] 8\n", - "[78, 84, 96, 2] 0\n", - "[117, 126, 144, 3] 8\n", - "[156, 168, 192, 4] -4\n", - "[195, 210, 240, 5] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (195, 210, 240, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 195\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 210\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 240\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 43, 15, 0] -103\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 43, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 44, 2, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 44, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 45, 14, 1] -4\n", - "[78, 90, 28, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 90, 28, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 45, 35, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 45, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 46, 9, 1] -8\n", - "[78, 92, 18, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 92, 18, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 48, 28, 1] 4\n", - "[78, 96, 56, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (78, 96, 56, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 78\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 78 * (103 - 78 )/103 =\n", - " = -103 + 156 * (25 )/103 =\n", - " = -103 + 156 * 25/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 56\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 49, 46, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 49, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 50, 19, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 50, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 51, 16, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (39, 51, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7265/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 0, 7, 1] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 0, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 1, 7, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 1, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 1, 16, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 1, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 2, 19, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 2, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 3, 26, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 3, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 4, 8, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 4, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 7, 32, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 7, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 7, 43, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 7, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 8, 3, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 8, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 9, 51, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 9, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 10, 47, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 10, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 11, 13, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 11, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 14, 48, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 14, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 15, 45, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 15, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 16, 43, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 16, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 17, 21, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 17, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 17, 50, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 17, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 18, 8, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 18, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 18, 28, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 18, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 19, 10, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 19, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 20, 6, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 20, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 22, 11, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 22, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 22, 29, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 22, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 23, 28, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 23, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 24, 25, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 24, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 25, 40, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 25, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 25, 46, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 25, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 26, 2, 1] -4\n", - "[80, 52, 4, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 52, 4, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 27, 46, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 27, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 28, 3, 1] -4\n", - "[80, 56, 6, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 56, 6, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 28, 27, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 28, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 29, 13, 1] 4\n", - "[80, 58, 26, 2] 0\n", - "[120, 87, 39, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (120, 87, 39, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 87\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 87 * (103 - 87 )/103 =\n", - " = -103 + 174 * (16 )/103 =\n", - " = -103 + 174 * 16/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 31, 17, 1] 8\n", - "[80, 62, 34, 2] 4\n", - "[120, 93, 51, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (120, 93, 51, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 93\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 31, 44, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 31, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 33, 2, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 33, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 34, 22, 1] 8\n", - "[80, 68, 44, 2] 4\n", - "[120, 102, 66, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (120, 102, 66, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 66\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 35, 48, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 35, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 37, 39, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 37, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 38, 16, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 38, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 39, 5, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 39, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 40, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 40, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 40, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 40, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 41, 9, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 41, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 41, 44, 1] 8\n", - "[80, 82, 88, 2] 8\n", - "[120, 123, 132, 3] 8\n", - "[160, 164, 176, 4] 4\n", - "[200, 205, 220, 5] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (200, 205, 220, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 200\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 97 * (103 - 97 )/103 =\n", - " = -103 + 194 * (6 )/103 =\n", - " = -103 + 194 * 6/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 205\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 220\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 42, 24, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 42, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 44, 50, 1] 8\n", - "[80, 88, 100, 2] 4\n", - "[120, 132, 150, 3] 0\n", - "[160, 176, 200, 4] -8\n", - "[200, 220, 250, 5] 4\n", - "[240, 264, 300, 6] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (240, 264, 300, 6)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 240\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 264\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 300\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 4\n", - "Sigma = 9857/103 ~ 95\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 45, 23, 1] 4\n", - "[80, 90, 46, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 90, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 45, 42, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 45, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 46, 1, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 46, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 46, 38, 1] 8\n", - "[80, 92, 76, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 92, 76, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 76\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 49, 9, 1] -8\n", - "[80, 98, 18, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (80, 98, 18, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 80\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 50, 30, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (40, 50, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -16\n", - "Sigma = -7217/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 1, 22, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 1, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 3, 39, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 3, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 6, 2, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 6, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 7, 4, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 7, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 7, 29, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 7, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 8, 49, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 8, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 9, 7, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 9, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 10, 45, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 10, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 12, 3, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 12, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 12, 27, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 12, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 13, 31, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 13, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 13, 41, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 13, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 14, 24, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 14, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 14, 36, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 14, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 16, 11, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 16, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 16, 29, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 16, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 17, 16, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 17, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 19, 15, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 19, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 20, 26, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 20, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 20, 33, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 20, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 21, 10, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 21, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 24, 21, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 24, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 24, 50, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 24, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 26, 5, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 26, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 26, 51, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 26, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 27, 39, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 27, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 28, 37, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 28, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 31, 1, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 31, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 31, 38, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 31, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 32, 8, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 32, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 33, 51, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 33, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 34, 14, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 34, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 35, 33, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 35, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 35, 36, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 35, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 36, 50, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 36, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 37, 10, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 37, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 38, 22, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 38, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 39, 47, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 39, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 40, 34, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 40, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 41, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 41, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 41, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 41, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 42, 17, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 42, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 43, 13, 1] -4\n", - "[82, 86, 26, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (82, 86, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 44, 7, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 44, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 44, 16, 1] 0\n", - "[82, 88, 32, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (82, 88, 32, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 45, 6, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 45, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 46, 34, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 46, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 47, 23, 1] 4\n", - "[82, 94, 46, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (82, 94, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 47, 42, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 47, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 49, 0, 1] 83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 49, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 50, 43, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (41, 50, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 51, 32, 1] 8\n", - "[82, 102, 64, 2] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (82, 102, 64, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 82\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 82 * (103 - 82 )/103 =\n", - " = -103 + 164 * (21 )/103 =\n", - " = -103 + 164 * 21/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -8\n", - "Sigma = -7989/103 ~ -77\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 64\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 0, 20, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 0, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 1, 20, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 1, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 1, 35, 1] 60\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 1, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 3, 10, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 3, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 4, 2, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 4, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 5, 42, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 5, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 6, 34, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 6, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 7, 6, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 7, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 8, 19, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 8, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 9, 45, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 9, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 12, 21, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 12, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 12, 50, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 12, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 14, 9, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 14, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 15, 25, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 15, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 16, 48, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 16, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 18, 38, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 18, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 20, 39, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 20, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 21, 4, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 21, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 21, 29, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 21, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 22, 33, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 22, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 22, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 22, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 23, 1, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 23, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 23, 38, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 23, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 24, 7, 1] 4\n", - "[84, 48, 14, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 48, 14, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 25, 32, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 25, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 25, 43, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 25, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 26, 47, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 26, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 27, 43, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 27, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 28, 16, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 28, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 29, 2, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 29, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 30, 8, 1] 0\n", - "[84, 60, 16, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 60, 16, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 30, 28, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 30, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 33, 47, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 33, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 35, 39, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 35, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 37, 11, 1] 0\n", - "[84, 74, 22, 2] 0\n", - "[126, 111, 33, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (126, 111, 33, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 126\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 37, 29, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 37, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 38, 14, 1] 0\n", - "[84, 76, 28, 2] 4\n", - "[126, 114, 42, 3] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (126, 114, 42, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 126\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -8\n", - "Sigma = -7753/103 ~ -75\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 38, 35, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 38, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 39, 13, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 39, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 42, 0, 0] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 42, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 42, 1, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 42, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 45, 40, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 45, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 45, 46, 1] 8\n", - "[84, 90, 92, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 90, 92, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 47, 31, 1] 8\n", - "[84, 94, 62, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 94, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 47, 41, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 47, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 48, 5, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 48, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 48, 51, 1] 8\n", - "[84, 96, 102, 2] 8\n", - "[126, 144, 153, 3] 0\n", - "[168, 192, 204, 4] 8\n", - "[210, 240, 255, 5] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (210, 240, 255, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 210\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = 0\n", - "Sigma = -9817/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 240\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 255\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 49, 15, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 49, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 50, 4, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 50, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 50, 18, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 50, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 51, 23, 1] 4\n", - "[84, 102, 46, 2] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (84, 102, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 51, 42, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (42, 51, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7133/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 1, 25, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 1, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 2, 3, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 2, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 3, 18, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 3, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 3, 23, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 3, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 5, 37, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 5, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 6, 12, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 6, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 7, 40, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 7, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 10, 38, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 10, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 11, 34, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 11, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 12, 47, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 12, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 13, 22, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 13, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 14, 43, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 14, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 15, 5, 1] 8\n", - "[86, 30, 10, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 30, 10, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 16, 40, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 16, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 16, 46, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 16, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 19, 26, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 19, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 20, 32, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 20, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 21, 31, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 21, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 23, 15, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 23, 15, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 24, 13, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 24, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 25, 42, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 25, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 26, 8, 1] 0\n", - "[86, 52, 16, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 52, 16, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 52\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 52 * (103 - 52 )/103 =\n", - " = -103 + 104 * (51 )/103 =\n", - " = -103 + 104 * 51/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 26, 28, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 26, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 27, 23, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 27, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 27, 42, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 27, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 28, 45, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 28, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 29, 34, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 29, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 30, 9, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 30, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 30, 44, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 30, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 32, 0, 1] 87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 32, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 33, 8, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 33, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 34, 21, 1] 4\n", - "[86, 68, 42, 2] 0\n", - "[129, 102, 63, 3] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (129, 102, 63, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 63\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 63 * (103 - 63 )/103 =\n", - " = -103 + 126 * (40 )/103 =\n", - " = -103 + 126 * 40/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 34, 50, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 34, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 35, 32, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 35, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 35, 43, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 35, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 36, 13, 1] -4\n", - "[86, 72, 26, 2] 0\n", - "[129, 108, 39, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (129, 108, 39, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 37, 6, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 37, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 38, 25, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 38, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 38, 27, 1] 8\n", - "[86, 76, 54, 2] 4\n", - "[129, 114, 81, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (129, 114, 81, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 40, 24, 1] 4\n", - "[86, 80, 48, 2] 8\n", - "[129, 120, 72, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (129, 120, 72, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 129\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 40, 36, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 40, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 41, 48, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 41, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 42, 11, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 42, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 42, 15, 1] -4\n", - "[86, 84, 30, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 84, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 84\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 43, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 43, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 43, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 43, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 46, 24, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 46, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 47, 19, 1] 0\n", - "[86, 94, 38, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 94, 38, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 49, 48, 1] 4\n", - "[86, 98, 96, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 98, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 50, 31, 1] 4\n", - "[86, 100, 62, 2] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 100, 62, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 62\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 50, 41, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (43, 50, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 51, 49, 1] 4\n", - "[86, 102, 98, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (86, 102, 98, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 1, 34, 1] 56\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 1, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 2, 5, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 2, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 2, 51, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 2, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 3, 37, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 3, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 4, 48, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 4, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 5, 47, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 5, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 6, 26, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 6, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 9, 0, 1] 115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 9, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 10, 11, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 10, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 10, 15, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 10, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 12, 28, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 12, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 15, 12, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 15, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 16, 22, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 16, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 17, 1, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 17, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 17, 38, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 17, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 18, 6, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 18, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 20, 3, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 20, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 21, 16, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 21, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 22, 14, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 22, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 23, 6, 1] 0\n", - "[88, 46, 12, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 46, 12, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 24, 17, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 24, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 24, 44, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 24, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 25, 21, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 25, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 25, 50, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 25, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 26, 39, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 26, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 27, 21, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 27, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 27, 37, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 27, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 29, 48, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 29, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 30, 32, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 30, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 30, 43, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 30, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 31, 40, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 31, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 31, 46, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 31, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 32, 4, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 32, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 32, 18, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 32, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 33, 9, 1] -4\n", - "[88, 66, 18, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 66, 18, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 36, 9, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 36, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 36, 44, 1] 8\n", - "[88, 72, 88, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 72, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 37, 19, 1] 4\n", - "[88, 74, 38, 2] 0\n", - "[132, 111, 57, 3] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (132, 111, 57, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 132\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 38, 34, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 38, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 39, 10, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 39, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 40, 30, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 40, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 41, 40, 1] 8\n", - "[88, 82, 80, 2] 4\n", - "[132, 123, 120, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (132, 123, 120, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 132\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -12\n", - "Sigma = -7553/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 123\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 120\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 42, 31, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 42, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 43, 4, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 43, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 43, 29, 1] 4\n", - "[88, 86, 58, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 86, 58, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 86\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 58\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 44, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 44, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 44, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 44, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 47, 45, 1] 4\n", - "[88, 94, 90, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 94, 90, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 48, 33, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 48, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 48, 36, 1] 4\n", - "[88, 96, 72, 2] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 96, 72, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 50, 7, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (44, 50, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 50, 16, 1] -4\n", - "[88, 100, 32, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (88, 100, 32, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 0, 6, 1] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 0, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 1, 6, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 1, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 4, 19, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 4, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 5, 24, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 5, 24, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 5, 36, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 5, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 6, 22, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 6, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 8, 10, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 8, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 9, 23, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 9, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 9, 42, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 9, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 10, 41, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 10, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 10, 49, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 10, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 12, 30, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 12, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 14, 5, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 14, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 14, 51, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 14, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 15, 40, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 15, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 17, 4, 1] 4\n", - "[90, 34, 8, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 34, 8, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 17, 18, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 17, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 18, 16, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 18, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 20, 34, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 20, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 21, 8, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 21, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 22, 2, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 22, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 23, 7, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 23, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 23, 16, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 23, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 24, 32, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 24, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 26, 14, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 26, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 28, 43, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 28, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 29, 19, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 29, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 30, 3, 1] -8\n", - "[90, 60, 6, 2] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 60, 6, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 30, 27, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 30, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 32, 21, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 32, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 32, 37, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 32, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 34, 26, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 34, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 34, 33, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 34, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 35, 5, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 35, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 37, 13, 1] -4\n", - "[90, 74, 26, 2] 0\n", - "[135, 111, 39, 3] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (135, 111, 39, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 135\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 111\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 38, 48, 1] 8\n", - "[90, 76, 96, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 76, 96, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 40, 20, 1] 0\n", - "[90, 80, 40, 2] 8\n", - "[135, 120, 60, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (135, 120, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 135\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -12\n", - "Sigma = -7301/103 ~ -70\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 41, 45, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 41, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 42, 7, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 42, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 43, 37, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 43, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 44, 18, 1] 0\n", - "[90, 88, 36, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 88, 36, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 88\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 44, 23, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 44, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 45, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 45, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 45, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 45, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 46, 20, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 46, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 46, 35, 1] 8\n", - "[90, 92, 70, 2] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 92, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 47, 9, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 47, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 47, 44, 1] 4\n", - "[90, 94, 88, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 94, 88, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 88\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 88 * (103 - 88 )/103 =\n", - " = -103 + 176 * (15 )/103 =\n", - " = -103 + 176 * 15/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 49, 45, 1] 4\n", - "[90, 98, 90, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (90, 98, 90, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -4\n", - "Sigma = -8681/103 ~ -84\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 50, 8, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 50, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 50, 28, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 50, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 51, 24, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (45, 51, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7449/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 1, 7, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 1, 7, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 2, 19, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 2, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 3, 46, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 3, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 4, 8, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 4, 8, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 4, 28, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 4, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 5, 22, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 5, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 6, 17, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 6, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 7, 32, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 7, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 8, 3, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 8, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 8, 27, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 8, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 9, 5, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 9, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 9, 51, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 9, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 11, 13, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 11, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 14, 48, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 14, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 15, 13, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 15, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 16, 32, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 16, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 16, 43, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 16, 43, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 17, 50, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 17, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 18, 28, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 18, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 19, 10, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 19, 10, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 20, 6, 1] 4\n", - "[92, 40, 12, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (92, 40, 12, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 21, 30, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 21, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 22, 4, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 22, 4, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 22, 29, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 22, 29, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 23, 24, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 23, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 25, 40, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 25, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 26, 38, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 26, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 27, 40, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 27, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 27, 46, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 27, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 28, 25, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 28, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 28, 27, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 28, 27, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 29, 8, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 29, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 31, 9, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 31, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 31, 44, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 31, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 32, 12, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 32, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 33, 2, 1] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 33, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 35, 6, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 35, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 36, 2, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 36, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 38, 7, 0] -111\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 38, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 38, 16, 1] 0\n", - "[92, 76, 32, 2] 0\n", - "[138, 114, 48, 3] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (138, 114, 48, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 138\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 39, 34, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 39, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 40, 0, 1] 83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 40, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 41, 9, 1] -8\n", - "[92, 82, 18, 2] 0\n", - "[138, 123, 27, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (138, 123, 27, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 138\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 123\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 42, 24, 1] 4\n", - "[92, 84, 48, 2] 8\n", - "[138, 126, 72, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (138, 126, 72, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 138\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 126\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 42, 36, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 42, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 44, 51, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 44, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 45, 42, 1] 8\n", - "[92, 90, 84, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (92, 90, 84, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 84\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 84 * (103 - 84 )/103 =\n", - " = -103 + 168 * (19 )/103 =\n", - " = -103 + 168 * 19/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 46, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 46, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 46, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 46, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 47, 14, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 47, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 49, 39, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (46, 49, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7425/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 50, 30, 1] 4\n", - "[92, 100, 60, 2] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (92, 100, 60, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 92\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 0, 26, 1] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 0, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 1, 26, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 1, 26, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 1, 33, 1] 56\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 1, 33, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 2, 24, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 2, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 3, 13, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 3, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 5, 17, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 5, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 5, 44, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 5, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 6, 14, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 6, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 7, 2, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 7, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 8, 11, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 8, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 8, 15, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 8, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 9, 6, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 9, 6, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 10, 40, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 10, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 11, 30, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 11, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 12, 43, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 12, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 15, 30, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 15, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 16, 2, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 16, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 17, 48, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 17, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 18, 22, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 18, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 19, 25, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 19, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 20, 47, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 20, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 22, 51, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 22, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 23, 22, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 23, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 24, 4, 1] -4\n", - "[94, 48, 8, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 48, 8, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 24, 18, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 24, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 25, 8, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 25, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 26, 42, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 26, 42, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 27, 13, 1] 4\n", - "[94, 54, 26, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 54, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 54\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 28, 11, 1] 4\n", - "[94, 56, 22, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 56, 22, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 28, 29, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 28, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 30, 37, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 30, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 31, 20, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 31, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 31, 35, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 31, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 32, 19, 1] 8\n", - "[94, 64, 38, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 64, 38, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 33, 23, 1] 8\n", - "[94, 66, 46, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 66, 46, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 66\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 66 * (103 - 66 )/103 =\n", - " = -103 + 132 * (37 )/103 =\n", - " = -103 + 132 * 37/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 33, 42, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 33, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 34, 9, 1] -4\n", - "[94, 68, 18, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 68, 18, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 68\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 35, 47, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 35, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 36, 18, 1] 4\n", - "[94, 72, 36, 2] -8\n", - "[141, 108, 54, 3] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (141, 108, 54, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 108\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 54\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 54 * (103 - 54 )/103 =\n", - " = -103 + 108 * (49 )/103 =\n", - " = -103 + 108 * 49/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 36, 23, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 36, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 38, 33, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 38, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 38, 36, 1] 8\n", - "[94, 76, 72, 2] -4\n", - "[141, 114, 108, 3] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (141, 114, 108, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 114\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 108\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 39, 31, 1] 8\n", - "[94, 78, 62, 2] 0\n", - "[141, 117, 93, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (141, 117, 93, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 117\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 93\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 39, 41, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 39, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 40, 3, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 40, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 41, 20, 1] 0\n", - "[94, 82, 40, 2] 4\n", - "[141, 123, 60, 3] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (141, 123, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 141\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -16\n", - "Sigma = -7317/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 123\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 43, 19, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 43, 19, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 44, 6, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 44, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 45, 34, 1] 8\n", - "[94, 90, 68, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (94, 90, 68, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 94\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "2. -T(2, 103), theta = 90\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 68\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 68 * (103 - 68 )/103 =\n", - " = -103 + 136 * (35 )/103 =\n", - " = -103 + 136 * 35/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 47, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 47, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 47, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 47, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 51, 17, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (47, 51, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 0, 13, 1] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 0, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 1, 13, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 1, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 4, 9, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 4, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 4, 44, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 4, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 5, 20, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 5, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 8, 51, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 8, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 10, 28, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 10, 28, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 11, 17, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 11, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 12, 2, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 12, 2, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 13, 21, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 13, 21, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 13, 50, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 13, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 14, 40, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 14, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 14, 46, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 14, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 16, 42, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 16, 42, 1)\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 17, 47, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 17, 47, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 18, 9, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 18, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 19, 18, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 19, 18, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 19, 23, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 19, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 22, 31, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 22, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 23, 39, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 23, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 24, 34, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 24, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 25, 22, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 25, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 28, 5, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 28, 5, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 28, 51, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 28, 51, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 29, 17, 1] 8\n", - "[96, 58, 34, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 58, 34, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 29, 44, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 29, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 30, 48, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 30, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 31, 10, 1] 0\n", - "[96, 62, 20, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 62, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 32, 33, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 32, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 32, 36, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 32, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 35, 40, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 35, 40, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 36, 34, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 36, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 38, 45, 1] 8\n", - "[96, 76, 90, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 76, 90, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 76\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 76 * (103 - 76 )/103 =\n", - " = -103 + 152 * (27 )/103 =\n", - " = -103 + 152 * 27/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 90\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 90 * (103 - 90 )/103 =\n", - " = -103 + 180 * (13 )/103 =\n", - " = -103 + 180 * 13/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 39, 12, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 39, 12, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 39\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 40, 11, 1] -4\n", - "[96, 80, 22, 2] -8\n", - "[144, 120, 33, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (144, 120, 33, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 120\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 40, 29, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 40, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 41, 43, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 41, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 42, 39, 1] 8\n", - "[96, 84, 78, 2] 0\n", - "[144, 126, 117, 3] 8\n", - "[192, 168, 156, 4] -4\n", - "[240, 210, 195, 5] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (240, 210, 195, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 240\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "2. -T(2, 103), theta = 210\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 195\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 43, 24, 1] 4\n", - "[96, 86, 48, 2] 4\n", - "[144, 129, 72, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (144, 129, 72, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 144\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -16\n", - "Sigma = -7173/103 ~ -69\n", - "\n", - "2. -T(2, 103), theta = 129\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 72\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 43, 36, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 43, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 45, 37, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 45, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 46, 11, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 46, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 46, 15, 1] -4\n", - "[96, 92, 30, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 92, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 47, 3, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 47, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 47, 27, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 47, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 48, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 48, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 48, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 48, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 49, 32, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 49, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 49, 43, 1] 8\n", - "[96, 98, 86, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 98, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 50, 14, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 50, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 51, 20, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (48, 51, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7389/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 51, 35, 1] 8\n", - "[96, 102, 70, 2] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (96, 102, 70, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 96\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 70\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 0, 22, 1] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 0, 22, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 1, 22, 0] -51\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 1, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 2, 30, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 2, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 3, 9, 1] 36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 3, 9, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 5, 32, 1] 48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 5, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 6, 2, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 6, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 7, 11, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 7, 11, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 7, 29, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 7, 29, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 29\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 8, 41, 1] 44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 8, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 8, 49, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 8, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 9, 7, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 9, 7, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 7\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = -9265/103 ~ -89\n", - "Satellite part = -4\n", - "Sigma = -9677/103 ~ -93\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 9, 16, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 9, 16, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 10, 45, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 10, 45, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 12, 3, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 12, 3, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 13, 31, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 13, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 14, 24, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 14, 24, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 15, 20, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 15, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 16, 11, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 16, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 16, 15, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 16, 15, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 15\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = -7969/103 ~ -77\n", - "Satellite part = -8\n", - "Sigma = -8793/103 ~ -85\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 17, 19, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 17, 19, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 19\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = -7417/103 ~ -72\n", - "Satellite part = -8\n", - "Sigma = -8241/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 20, 33, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 20, 33, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 33\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = -5989/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7637/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 20, 36, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 20, 36, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 21, 10, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 21, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 22, 12, 1] 8\n", - "[98, 44, 24, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 44, 24, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 24\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = -6817/103 ~ -66\n", - "Satellite part = -12\n", - "Sigma = -8053/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 24, 21, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 24, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 24, 37, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 24, 37, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 25, 39, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 25, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 26, 51, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 26, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 27, 39, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 27, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 28, 49, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 28, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 31, 38, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 31, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 32, 13, 1] 0\n", - "[98, 64, 26, 2] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 64, 26, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 33, 50, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 33, 50, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 35, 24, 1] 8\n", - "[98, 70, 48, 2] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 70, 48, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 70\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 70 * (103 - 70 )/103 =\n", - " = -103 + 140 * (33 )/103 =\n", - " = -103 + 140 * 33/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 35, 36, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 35, 36, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 36, 21, 1] 4\n", - "[98, 72, 42, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 72, 42, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 72\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 72 * (103 - 72 )/103 =\n", - " = -103 + 144 * (31 )/103 =\n", - " = -103 + 144 * 31/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 36, 50, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 36, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 40, 34, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 40, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 41, 1, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 41, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 41, 38, 1] 8\n", - "[98, 82, 76, 2] -4\n", - "[147, 123, 114, 3] 8\n", - "[196, 164, 152, 4] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (196, 164, 152, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 196\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 93 * (103 - 93 )/103 =\n", - " = -103 + 186 * (10 )/103 =\n", - " = -103 + 186 * 10/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "2. -T(2, 103), theta = 164\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 61 * (103 - 61 )/103 =\n", - " = -103 + 122 * (42 )/103 =\n", - " = -103 + 122 * 42/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 152\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 43, 13, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 43, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 44, 16, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 44, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 45, 6, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 45, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 45\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 46, 5, 1] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 46, 5, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 5\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 47, 18, 1] 0\n", - "[98, 94, 36, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 94, 36, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 36\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = -5785/103 ~ -56\n", - "Satellite part = -20\n", - "Sigma = -7845/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 47, 23, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 47, 23, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 48, 25, 1] 4\n", - "[98, 96, 50, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 96, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 96\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 96 * (103 - 96 )/103 =\n", - " = -103 + 192 * (7 )/103 =\n", - " = -103 + 192 * 7/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 49, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 49, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 49, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 49, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 50, 10, 1] -8\n", - "[98, 100, 20, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 100, 20, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 100\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 51, 32, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (49, 51, 32, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 51, 43, 1] 8\n", - "[98, 102, 86, 2] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (98, 102, 86, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 98\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = -9629/103 ~ -93\n", - "Satellite part = -4\n", - "Sigma = -10041/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 102\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 86\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 86 * (103 - 86 )/103 =\n", - " = -103 + 172 * (17 )/103 =\n", - " = -103 + 172 * 17/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 0, 30, 1] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 0, 30, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 0\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 1, 30, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 1, 30, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 2, 39, 0] -47\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 2, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 4, 20, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 4, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 4, 35, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 4, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 5, 10, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 5, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 6, 3, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 6, 3, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 3\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 6, 27, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 6, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 6\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = 9445/103 ~ 91\n", - "Satellite part = 0\n", - "Sigma = 9445/103 ~ 91\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 8, 6, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 8, 6, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 10, 22, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 10, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 10\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = 8749/103 ~ 84\n", - "Satellite part = 0\n", - "Sigma = 8749/103 ~ 84\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 11, 14, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 11, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 11\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 12, 23, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 12, 23, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 23\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = -6929/103 ~ -67\n", - "Satellite part = -12\n", - "Sigma = -8165/103 ~ -79\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 12, 42, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 12, 42, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 13, 48, 0] -67\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 13, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 14, 13, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 14, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 16, 34, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 16, 34, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 16\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = 7825/103 ~ 75\n", - "Satellite part = 0\n", - "Sigma = 7825/103 ~ 75\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 17, 40, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 17, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 17, 46, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 17, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 18, 20, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 18, 20, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 19, 5, 1] 4\n", - "[100, 38, 10, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 38, 10, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 20, 8, 1] 8\n", - "[100, 40, 16, 2] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 40, 16, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 20, 28, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 20, 28, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 21, 1, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 21, 1, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 21, 38, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 21, 38, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 21\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = 7165/103 ~ 69\n", - "Satellite part = 0\n", - "Sigma = 7165/103 ~ 69\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 24, 31, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 24, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 24, 41, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 24, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 24\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 24 * (103 - 24 )/103 =\n", - " = -103 + 48 * (79 )/103 =\n", - " = -103 + 48 * 79/103 = \n", - " = -103 + 3792/103 = \n", - " = -6817/103 \n", - "Pattern part = 6817/103 ~ 66\n", - "Satellite part = 0\n", - "Sigma = 6817/103 ~ 66\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 25, 17, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 25, 17, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 25, 44, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 25, 44, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 25\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = 6709/103 ~ 65\n", - "Satellite part = 0\n", - "Sigma = 6709/103 ~ 65\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 26, 37, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 26, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 27, 17, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 27, 17, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 27\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = 6505/103 ~ 63\n", - "Satellite part = 0\n", - "Sigma = 6505/103 ~ 63\n", - "\n", - "3. T(2, 13; 2, 103), theta = 17\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = -7685/103 ~ -74\n", - "Satellite part = -8\n", - "Sigma = -8509/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 28, 6, 1] -4\n", - "[100, 56, 12, 2] -36\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 56, 12, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 56\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 56 * (103 - 56 )/103 =\n", - " = -103 + 112 * (47 )/103 =\n", - " = -103 + 112 * 47/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 29, 14, 1] 4\n", - "[100, 58, 28, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 58, 28, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 58\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 58 * (103 - 58 )/103 =\n", - " = -103 + 116 * (45 )/103 =\n", - " = -103 + 116 * 45/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = 5389/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5389/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 28\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = -6409/103 ~ -62\n", - "Satellite part = -16\n", - "Sigma = -8057/103 ~ -78\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 29, 35, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 29, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 29\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 29 * (103 - 29 )/103 =\n", - " = -103 + 58 * (74 )/103 =\n", - " = -103 + 58 * 74/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = 6317/103 ~ 61\n", - "Satellite part = 0\n", - "Sigma = 6317/103 ~ 61\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 30, 7, 1] -4\n", - "[100, 60, 14, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 60, 14, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 60\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 31, 25, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 31, 25, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 33, 49, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 33, 49, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 34, 43, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 34, 43, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 43\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 35, 8, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 35, 8, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 8\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = -9089/103 ~ -88\n", - "Satellite part = -4\n", - "Sigma = -9501/103 ~ -92\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 36, 41, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 36, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 36, 49, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 36, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 37, 38, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 37, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 39, 19, 1] 4\n", - "[100, 78, 38, 2] -8\n", - "[150, 117, 57, 3] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (150, 117, 57, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 150\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7405/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 117\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 57\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 40, 50, 1] 8\n", - "[100, 80, 100, 2] -28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 80, 100, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 44, 40, 1] 8\n", - "[100, 88, 80, 2] 0\n", - "[150, 132, 120, 3] 4\n", - "[200, 176, 160, 4] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (200, 176, 160, 4)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 200\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 97 * (103 - 97 )/103 =\n", - " = -103 + 194 * (6 )/103 =\n", - " = -103 + 194 * 6/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "2. -T(2, 103), theta = 176\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 73 * (103 - 73 )/103 =\n", - " = -103 + 146 * (30 )/103 =\n", - " = -103 + 146 * 30/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 160\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 57 * (103 - 57 )/103 =\n", - " = -103 + 114 * (46 )/103 =\n", - " = -103 + 114 * 46/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 4\n", - "Sigma = 10229/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 45, 12, 1] -8\n", - "[100, 90, 24, 2] 4\n", - "[150, 135, 36, 3] 8\n", - "[200, 180, 48, 4] -8\n", - "[250, 225, 60, 5] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (250, 225, 60, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 250\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7477/103 ~ -72\n", - "\n", - "2. -T(2, 103), theta = 225\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 46, 21, 1] 0\n", - "[100, 92, 42, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 92, 42, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 92\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 92 * (103 - 92 )/103 =\n", - " = -103 + 184 * (11 )/103 =\n", - " = -103 + 184 * 11/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = 8585/103 ~ 83\n", - "Satellite part = 0\n", - "Sigma = 8585/103 ~ 83\n", - "\n", - "3. T(2, 13; 2, 103), theta = 42\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = -5485/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7545/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 46, 50, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 46, 50, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 47, 11, 0] -107\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 47, 11, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 47\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = 5345/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5345/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 11\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 11 * (103 - 11 )/103 =\n", - " = -103 + 22 * (92 )/103 =\n", - " = -103 + 22 * 92/103 = \n", - " = -103 + 2024/103 = \n", - " = -8585/103 \n", - "Pattern part = -8585/103 ~ -83\n", - "Satellite part = -4\n", - "Sigma = -8997/103 ~ -87\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 47, 15, 1] -4\n", - "[100, 94, 30, 2] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (100, 94, 30, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 100\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 100 * (103 - 100 )/103 =\n", - " = -103 + 200 * (3 )/103 =\n", - " = -103 + 200 * 3/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = -10009/103 ~ -97\n", - "Satellite part = 0\n", - "Sigma = -10009/103 ~ -97\n", - "\n", - "2. -T(2, 103), theta = 94\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 94 * (103 - 94 )/103 =\n", - " = -103 + 188 * (9 )/103 =\n", - " = -103 + 188 * 9/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 30\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = -6229/103 ~ -60\n", - "Satellite part = -16\n", - "Sigma = -7877/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 49, 2, 0] -119\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 49, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 49\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = 5317/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5317/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 50, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 50, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 50, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (50, 50, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 1, 39, 1] 56\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 1, 39, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 2, 9, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 2, 9, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 9\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = -8917/103 ~ -86\n", - "Satellite part = -4\n", - "Sigma = -9329/103 ~ -90\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 2, 44, 1] 52\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 2, 44, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 4, 14, 0] -63\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 4, 14, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 4\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = 9817/103 ~ 95\n", - "Satellite part = 0\n", - "Sigma = 9817/103 ~ 95\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 5, 0, 1] 123\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 5, 0, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 7, 34, 0] -55\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 7, 34, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 7\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 7 * (103 - 7 )/103 =\n", - " = -103 + 14 * (96 )/103 =\n", - " = -103 + 14 * 96/103 = \n", - " = -103 + 1344/103 = \n", - " = -9265/103 \n", - "Pattern part = 9265/103 ~ 89\n", - "Satellite part = 0\n", - "Sigma = 9265/103 ~ 89\n", - "\n", - "3. T(2, 13; 2, 103), theta = 34\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = -5917/103 ~ -57\n", - "Satellite part = -16\n", - "Sigma = -7565/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 8, 48, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 8, 48, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 8\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 8 * (103 - 8 )/103 =\n", - " = -103 + 16 * (95 )/103 =\n", - " = -103 + 16 * 95/103 = \n", - " = -103 + 1520/103 = \n", - " = -9089/103 \n", - "Pattern part = 9089/103 ~ 88\n", - "Satellite part = 0\n", - "Sigma = 9089/103 ~ 88\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 9, 40, 0] -59\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 9, 40, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 40\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = -5569/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7629/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 9, 46, 1] 40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 9, 46, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 9\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 9 * (103 - 9 )/103 =\n", - " = -103 + 18 * (94 )/103 =\n", - " = -103 + 18 * 94/103 = \n", - " = -103 + 1692/103 = \n", - " = -8917/103 \n", - "Pattern part = 8917/103 ~ 86\n", - "Satellite part = 0\n", - "Sigma = 8917/103 ~ 86\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 12, 4, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 12, 4, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 12, 18, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 12, 18, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 12\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = 8425/103 ~ 81\n", - "Satellite part = 0\n", - "Sigma = 8425/103 ~ 81\n", - "\n", - "3. T(2, 13; 2, 103), theta = 18\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = -7549/103 ~ -73\n", - "Satellite part = -8\n", - "Sigma = -8373/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 13, 12, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 13, 12, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 13\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = 8269/103 ~ 80\n", - "Satellite part = 0\n", - "Sigma = 8269/103 ~ 80\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 14, 45, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 14, 45, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 14\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = 8117/103 ~ 78\n", - "Satellite part = 0\n", - "Sigma = 8117/103 ~ 78\n", - "\n", - "3. T(2, 13; 2, 103), theta = 45\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 45 * (103 - 45 )/103 =\n", - " = -103 + 90 * (58 )/103 =\n", - " = -103 + 90 * 58/103 = \n", - " = -103 + 5220/103 = \n", - " = -5389/103 \n", - "Pattern part = -5389/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7861/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 15, 32, 1] 32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 15, 32, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 15\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 15 * (103 - 15 )/103 =\n", - " = -103 + 30 * (88 )/103 =\n", - " = -103 + 30 * 88/103 = \n", - " = -103 + 2640/103 = \n", - " = -7969/103 \n", - "Pattern part = 7969/103 ~ 77\n", - "Satellite part = 0\n", - "Sigma = 7969/103 ~ 77\n", - "\n", - "3. T(2, 13; 2, 103), theta = 32\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = -6065/103 ~ -58\n", - "Satellite part = -16\n", - "Sigma = -7713/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 16, 5, 1] 8\n", - "[102, 32, 10, 2] -32\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 32, 10, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 32\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 32 * (103 - 32 )/103 =\n", - " = -103 + 64 * (71 )/103 =\n", - " = -103 + 64 * 71/103 = \n", - " = -103 + 4544/103 = \n", - " = -6065/103 \n", - "Pattern part = 6065/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 6065/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 17, 26, 1] 28\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 17, 26, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 17\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 17 * (103 - 17 )/103 =\n", - " = -103 + 34 * (86 )/103 =\n", - " = -103 + 34 * 86/103 = \n", - " = -103 + 2924/103 = \n", - " = -7685/103 \n", - "Pattern part = 7685/103 ~ 74\n", - "Satellite part = 0\n", - "Sigma = 7685/103 ~ 74\n", - "\n", - "3. T(2, 13; 2, 103), theta = 26\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = -6605/103 ~ -64\n", - "Satellite part = -12\n", - "Sigma = -7841/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 18, 14, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 18, 14, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 14\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 14 * (103 - 14 )/103 =\n", - " = -103 + 28 * (89 )/103 =\n", - " = -103 + 28 * 89/103 = \n", - " = -103 + 2492/103 = \n", - " = -8117/103 \n", - "Pattern part = -8117/103 ~ -78\n", - "Satellite part = -8\n", - "Sigma = -8941/103 ~ -86\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 18, 35, 0] -71\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 18, 35, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 18\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 18 * (103 - 18 )/103 =\n", - " = -103 + 36 * (85 )/103 =\n", - " = -103 + 36 * 85/103 = \n", - " = -103 + 3060/103 = \n", - " = -7549/103 \n", - "Pattern part = 7549/103 ~ 73\n", - "Satellite part = 0\n", - "Sigma = 7549/103 ~ 73\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 19, 51, 0] -75\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 19, 51, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 19\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 19 * (103 - 19 )/103 =\n", - " = -103 + 38 * (84 )/103 =\n", - " = -103 + 38 * 84/103 = \n", - " = -103 + 3192/103 = \n", - " = -7417/103 \n", - "Pattern part = 7417/103 ~ 72\n", - "Satellite part = 0\n", - "Sigma = 7417/103 ~ 72\n", - "\n", - "3. T(2, 13; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7777/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 20, 13, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 20, 13, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 20\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 21, 2, 1] 0\n", - "[102, 42, 4, 2] -48\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 42, 4, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 42\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 42 * (103 - 42 )/103 =\n", - " = -103 + 84 * (61 )/103 =\n", - " = -103 + 84 * 61/103 = \n", - " = -103 + 5124/103 = \n", - " = -5485/103 \n", - "Pattern part = 5485/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5485/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 4\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 22, 47, 0] -79\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 22, 47, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 22\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = 7045/103 ~ 68\n", - "Satellite part = 0\n", - "Sigma = 7045/103 ~ 68\n", - "\n", - "3. T(2, 13; 2, 103), theta = 47\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 47 * (103 - 47 )/103 =\n", - " = -103 + 94 * (56 )/103 =\n", - " = -103 + 94 * 56/103 = \n", - " = -103 + 5264/103 = \n", - " = -5345/103 \n", - "Pattern part = -5345/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7817/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 23, 20, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 23, 20, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 20\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = -7289/103 ~ -70\n", - "Satellite part = -12\n", - "Sigma = -8525/103 ~ -82\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 23, 35, 1] 24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 23, 35, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 23\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 35\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = -5849/103 ~ -56\n", - "Satellite part = -16\n", - "Sigma = -7497/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 24, 6, 1] 0\n", - "[102, 48, 12, 2] -40\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 48, 12, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 48\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = 5329/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5329/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 12\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 12 * (103 - 12 )/103 =\n", - " = -103 + 24 * (91 )/103 =\n", - " = -103 + 24 * 91/103 = \n", - " = -103 + 2184/103 = \n", - " = -8425/103 \n", - "Pattern part = -8425/103 ~ -81\n", - "Satellite part = -8\n", - "Sigma = -9249/103 ~ -89\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 26, 41, 1] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 26, 41, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 26, 49, 0] -83\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 26, 49, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 26\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 26 * (103 - 26 )/103 =\n", - " = -103 + 52 * (77 )/103 =\n", - " = -103 + 52 * 77/103 = \n", - " = -103 + 4004/103 = \n", - " = -6605/103 \n", - "Pattern part = 6605/103 ~ 64\n", - "Satellite part = 0\n", - "Sigma = 6605/103 ~ 64\n", - "\n", - "3. T(2, 13; 2, 103), theta = 49\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7789/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 28, 48, 1] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 28, 48, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 28\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 28 * (103 - 28 )/103 =\n", - " = -103 + 56 * (75 )/103 =\n", - " = -103 + 56 * 75/103 = \n", - " = -103 + 4200/103 = \n", - " = -6409/103 \n", - "Pattern part = 6409/103 ~ 62\n", - "Satellite part = 0\n", - "Sigma = 6409/103 ~ 62\n", - "\n", - "3. T(2, 13; 2, 103), theta = 48\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 48 * (103 - 48 )/103 =\n", - " = -103 + 96 * (55 )/103 =\n", - " = -103 + 96 * 55/103 = \n", - " = -103 + 5280/103 = \n", - " = -5329/103 \n", - "Pattern part = -5329/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7801/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 30, 16, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 30, 16, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 30\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 30 * (103 - 30 )/103 =\n", - " = -103 + 60 * (73 )/103 =\n", - " = -103 + 60 * 73/103 = \n", - " = -103 + 4380/103 = \n", - " = -6229/103 \n", - "Pattern part = 6229/103 ~ 60\n", - "Satellite part = 0\n", - "Sigma = 6229/103 ~ 60\n", - "\n", - "3. T(2, 13; 2, 103), theta = 16\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 16 * (103 - 16 )/103 =\n", - " = -103 + 32 * (87 )/103 =\n", - " = -103 + 32 * 87/103 = \n", - " = -103 + 2784/103 = \n", - " = -7825/103 \n", - "Pattern part = -7825/103 ~ -75\n", - "Satellite part = -8\n", - "Sigma = -8649/103 ~ -83\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 31, 3, 1] -8\n", - "[102, 62, 6, 2] -44\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 62, 6, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 62\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 62 * (103 - 62 )/103 =\n", - " = -103 + 124 * (41 )/103 =\n", - " = -103 + 124 * 41/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 6\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 6 * (103 - 6 )/103 =\n", - " = -103 + 12 * (97 )/103 =\n", - " = -103 + 12 * 97/103 = \n", - " = -103 + 1164/103 = \n", - " = -9445/103 \n", - "Pattern part = -9445/103 ~ -91\n", - "Satellite part = -4\n", - "Sigma = -9857/103 ~ -95\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 31, 27, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 31, 27, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 31\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = 6145/103 ~ 59\n", - "Satellite part = 0\n", - "Sigma = 6145/103 ~ 59\n", - "\n", - "3. T(2, 13; 2, 103), theta = 27\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 27 * (103 - 27 )/103 =\n", - " = -103 + 54 * (76 )/103 =\n", - " = -103 + 54 * 76/103 = \n", - " = -103 + 4104/103 = \n", - " = -6505/103 \n", - "Pattern part = -6505/103 ~ -63\n", - "Satellite part = -12\n", - "Sigma = -7741/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 32, 22, 1] 8\n", - "[102, 64, 44, 2] -24\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 64, 44, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 64\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 64 * (103 - 64 )/103 =\n", - " = -103 + 128 * (39 )/103 =\n", - " = -103 + 128 * 39/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = 5617/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5617/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 44\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = -5417/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7889/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 33, 31, 1] 12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 33, 31, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 33, 41, 0] -87\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 33, 41, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 33\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 33 * (103 - 33 )/103 =\n", - " = -103 + 66 * (70 )/103 =\n", - " = -103 + 66 * 70/103 = \n", - " = -103 + 4620/103 = \n", - " = -5989/103 \n", - "Pattern part = 5989/103 ~ 58\n", - "Satellite part = 0\n", - "Sigma = 5989/103 ~ 58\n", - "\n", - "3. T(2, 13; 2, 103), theta = 41\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = -5525/103 ~ -53\n", - "Satellite part = -20\n", - "Sigma = -7585/103 ~ -73\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 34, 10, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 34, 10, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 34\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 10\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 10 * (103 - 10 )/103 =\n", - " = -103 + 20 * (93 )/103 =\n", - " = -103 + 20 * 93/103 = \n", - " = -103 + 1860/103 = \n", - " = -8749/103 \n", - "Pattern part = -8749/103 ~ -84\n", - "Satellite part = -4\n", - "Sigma = -9161/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 35, 13, 0] -103\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 35, 13, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 35\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 35 * (103 - 35 )/103 =\n", - " = -103 + 70 * (68 )/103 =\n", - " = -103 + 70 * 68/103 = \n", - " = -103 + 4760/103 = \n", - " = -5849/103 \n", - "Pattern part = 5849/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5849/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 13\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 13 * (103 - 13 )/103 =\n", - " = -103 + 26 * (90 )/103 =\n", - " = -103 + 26 * 90/103 = \n", - " = -103 + 2340/103 = \n", - " = -8269/103 \n", - "Pattern part = -8269/103 ~ -80\n", - "Satellite part = -8\n", - "Sigma = -9093/103 ~ -88\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 36, 31, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 36, 31, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 36\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 36 * (103 - 36 )/103 =\n", - " = -103 + 72 * (67 )/103 =\n", - " = -103 + 72 * 67/103 = \n", - " = -103 + 4824/103 = \n", - " = -5785/103 \n", - "Pattern part = 5785/103 ~ 56\n", - "Satellite part = 0\n", - "Sigma = 5785/103 ~ 56\n", - "\n", - "3. T(2, 13; 2, 103), theta = 31\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 31 * (103 - 31 )/103 =\n", - " = -103 + 62 * (72 )/103 =\n", - " = -103 + 62 * 72/103 = \n", - " = -103 + 4464/103 = \n", - " = -6145/103 \n", - "Pattern part = -6145/103 ~ -59\n", - "Satellite part = -16\n", - "Sigma = -7793/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 37, 2, 0] -115\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 37, 2, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 37\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = 5725/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5725/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 2\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = -10205/103 ~ -99\n", - "Satellite part = 0\n", - "Sigma = -10205/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 38, 39, 0] -91\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 38, 39, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 38\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = 5669/103 ~ 55\n", - "Satellite part = 0\n", - "Sigma = 5669/103 ~ 55\n", - "\n", - "3. T(2, 13; 2, 103), theta = 39\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 39 * (103 - 39 )/103 =\n", - " = -103 + 78 * (64 )/103 =\n", - " = -103 + 78 * 64/103 = \n", - " = -103 + 4992/103 = \n", - " = -5617/103 \n", - "Pattern part = -5617/103 ~ -54\n", - "Satellite part = -20\n", - "Sigma = -7677/103 ~ -74\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 40, 21, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 40, 21, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 40\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 40 * (103 - 40 )/103 =\n", - " = -103 + 80 * (63 )/103 =\n", - " = -103 + 80 * 63/103 = \n", - " = -103 + 5040/103 = \n", - " = -5569/103 \n", - "Pattern part = 5569/103 ~ 54\n", - "Satellite part = 0\n", - "Sigma = 5569/103 ~ 54\n", - "\n", - "3. T(2, 13; 2, 103), theta = 21\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 21 * (103 - 21 )/103 =\n", - " = -103 + 42 * (82 )/103 =\n", - " = -103 + 42 * 82/103 = \n", - " = -103 + 3444/103 = \n", - " = -7165/103 \n", - "Pattern part = -7165/103 ~ -69\n", - "Satellite part = -12\n", - "Sigma = -8401/103 ~ -81\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 40, 37, 1] 8\n", - "[102, 80, 74, 2] -12\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 80, 74, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 80\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 80 * (103 - 80 )/103 =\n", - " = -103 + 160 * (23 )/103 =\n", - " = -103 + 160 * 23/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 74\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 74 * (103 - 74 )/103 =\n", - " = -103 + 148 * (29 )/103 =\n", - " = -103 + 148 * 29/103 = \n", - " = -103 + 4292/103 = \n", - " = -6317/103 \n", - "Pattern part = -6317/103 ~ -61\n", - "Satellite part = -16\n", - "Sigma = -7965/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 41, 25, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 41, 25, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 41\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 41 * (103 - 41 )/103 =\n", - " = -103 + 82 * (62 )/103 =\n", - " = -103 + 82 * 62/103 = \n", - " = -103 + 5084/103 = \n", - " = -5525/103 \n", - "Pattern part = 5525/103 ~ 53\n", - "Satellite part = 0\n", - "Sigma = 5525/103 ~ 53\n", - "\n", - "3. T(2, 13; 2, 103), theta = 25\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 25 * (103 - 25 )/103 =\n", - " = -103 + 50 * (78 )/103 =\n", - " = -103 + 50 * 78/103 = \n", - " = -103 + 3900/103 = \n", - " = -6709/103 \n", - "Pattern part = -6709/103 ~ -65\n", - "Satellite part = -12\n", - "Sigma = -7945/103 ~ -77\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 41, 27, 1] 8\n", - "[102, 82, 54, 2] -8\n", - "[153, 123, 81, 3] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (153, 123, 81, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 153\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 123\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 20 * (103 - 20 )/103 =\n", - " = -103 + 40 * (83 )/103 =\n", - " = -103 + 40 * 83/103 = \n", - " = -103 + 3320/103 = \n", - " = -7289/103 \n", - "Pattern part = 7289/103 ~ 70\n", - "Satellite part = 0\n", - "Sigma = 7289/103 ~ 70\n", - "\n", - "3. T(2, 13; 2, 103), theta = 81\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 81 * (103 - 81 )/103 =\n", - " = -103 + 162 * (22 )/103 =\n", - " = -103 + 162 * 22/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 42, 20, 1] 0\n", - "[102, 84, 40, 2] -4\n", - "[153, 126, 60, 3] 20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (153, 126, 60, 3)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 153\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7369/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 126\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 23 * (103 - 23 )/103 =\n", - " = -103 + 46 * (80 )/103 =\n", - " = -103 + 46 * 80/103 = \n", - " = -103 + 3680/103 = \n", - " = -6929/103 \n", - "Pattern part = 6929/103 ~ 67\n", - "Satellite part = 0\n", - "Sigma = 6929/103 ~ 67\n", - "\n", - "3. T(2, 13; 2, 103), theta = 60\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 60 * (103 - 60 )/103 =\n", - " = -103 + 120 * (43 )/103 =\n", - " = -103 + 120 * 43/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = -5449/103 ~ -52\n", - "Satellite part = -20\n", - "Sigma = -7509/103 ~ -72\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 3\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 3 * (103 - 3 )/103 =\n", - " = -103 + 6 * (100 )/103 =\n", - " = -103 + 6 * 100/103 = \n", - " = -103 + 600/103 = \n", - " = -10009/103 \n", - "Pattern part = 10009/103 ~ 97\n", - "Satellite part = 0\n", - "Sigma = 10009/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 43, 22, 0] -99\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 43, 22, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 43\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 43 * (103 - 43 )/103 =\n", - " = -103 + 86 * (60 )/103 =\n", - " = -103 + 86 * 60/103 = \n", - " = -103 + 5160/103 = \n", - " = -5449/103 \n", - "Pattern part = 5449/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5449/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 22\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 22 * (103 - 22 )/103 =\n", - " = -103 + 44 * (81 )/103 =\n", - " = -103 + 44 * 81/103 = \n", - " = -103 + 3564/103 = \n", - " = -7045/103 \n", - "Pattern part = -7045/103 ~ -68\n", - "Satellite part = -12\n", - "Sigma = -8281/103 ~ -80\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 44, 46, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 44, 46, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 44\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 44 * (103 - 44 )/103 =\n", - " = -103 + 88 * (59 )/103 =\n", - " = -103 + 88 * 59/103 = \n", - " = -103 + 5192/103 = \n", - " = -5417/103 \n", - "Pattern part = 5417/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5417/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 46\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = -5365/103 ~ -52\n", - "Satellite part = -24\n", - "Sigma = -7837/103 ~ -76\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 46, 37, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 46, 37, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 46\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 46 * (103 - 46 )/103 =\n", - " = -103 + 92 * (57 )/103 =\n", - " = -103 + 92 * 57/103 = \n", - " = -103 + 5244/103 = \n", - " = -5365/103 \n", - "Pattern part = 5365/103 ~ 52\n", - "Satellite part = 0\n", - "Sigma = 5365/103 ~ 52\n", - "\n", - "3. T(2, 13; 2, 103), theta = 37\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 37 * (103 - 37 )/103 =\n", - " = -103 + 74 * (66 )/103 =\n", - " = -103 + 74 * 66/103 = \n", - " = -103 + 4884/103 = \n", - " = -5725/103 \n", - "Pattern part = -5725/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7785/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 48, 42, 1] 8\n", - "[102, 96, 84, 2] 8\n", - "[153, 144, 126, 3] 0\n", - "[204, 192, 168, 4] 4\n", - "[255, 240, 210, 5] -16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (255, 240, 210, 5)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 255\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 49 * (103 - 49 )/103 =\n", - " = -103 + 98 * (54 )/103 =\n", - " = -103 + 98 * 54/103 = \n", - " = -103 + 5292/103 = \n", - " = -5317/103 \n", - "Pattern part = -5317/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7377/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 240\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 34 * (103 - 34 )/103 =\n", - " = -103 + 68 * (69 )/103 =\n", - " = -103 + 68 * 69/103 = \n", - " = -103 + 4692/103 = \n", - " = -5917/103 \n", - "Pattern part = 5917/103 ~ 57\n", - "Satellite part = 0\n", - "Sigma = 5917/103 ~ 57\n", - "\n", - "3. T(2, 13; 2, 103), theta = 210\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 4 * (103 - 4 )/103 =\n", - " = -103 + 8 * (99 )/103 =\n", - " = -103 + 8 * 99/103 = \n", - " = -103 + 792/103 = \n", - " = -9817/103 \n", - "Pattern part = -9817/103 ~ -95\n", - "Satellite part = -4\n", - "Sigma = -10229/103 ~ -99\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 5\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 5 * (103 - 5 )/103 =\n", - " = -103 + 10 * (98 )/103 =\n", - " = -103 + 10 * 98/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 4\n", - "Sigma = 10041/103 ~ 97\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 49, 25, 1] 4\n", - "[102, 98, 50, 2] 16\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (102, 98, 50, 2)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 102\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 102 * (103 - 102 )/103 =\n", - " = -103 + 204 * (1 )/103 =\n", - " = -103 + 204 * 1/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "2. -T(2, 103), theta = 98\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 98 * (103 - 98 )/103 =\n", - " = -103 + 196 * (5 )/103 =\n", - " = -103 + 196 * 5/103 = \n", - " = -103 + 980/103 = \n", - " = -9629/103 \n", - "Pattern part = 9629/103 ~ 93\n", - "Satellite part = 0\n", - "Sigma = 9629/103 ~ 93\n", - "\n", - "3. T(2, 13; 2, 103), theta = 50\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = -5309/103 ~ -51\n", - "Satellite part = -24\n", - "Sigma = -7781/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 2\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 2 * (103 - 2 )/103 =\n", - " = -103 + 4 * (101 )/103 =\n", - " = -103 + 4 * 101/103 = \n", - " = -103 + 404/103 = \n", - " = -10205/103 \n", - "Pattern part = 10205/103 ~ 99\n", - "Satellite part = 0\n", - "Sigma = 10205/103 ~ 99\n", - "\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 50, 38, 0] -95\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 50, 38, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 50\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 50 * (103 - 50 )/103 =\n", - " = -103 + 100 * (53 )/103 =\n", - " = -103 + 100 * 53/103 = \n", - " = -103 + 5300/103 = \n", - " = -5309/103 \n", - "Pattern part = 5309/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5309/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 38\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 38 * (103 - 38 )/103 =\n", - " = -103 + 76 * (65 )/103 =\n", - " = -103 + 76 * 65/103 = \n", - " = -103 + 4940/103 = \n", - " = -5669/103 \n", - "Pattern part = -5669/103 ~ -55\n", - "Satellite part = -20\n", - "Sigma = -7729/103 ~ -75\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 51, 0, 0] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 51, 0, 0)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 0\n", - "4. -T(2, 17; 2, 103), theta = 0\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 51, 1, 1] -20\n", - "Calculation details for a cable sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "and theta vector: (51, 51, 1, 1)\n", - "\n", - "1. T(2, 11; 2, 103), theta = 51\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = -5305/103 ~ -51\n", - "Satellite part = -20\n", - "Sigma = -7365/103 ~ -71\n", - "\n", - "2. -T(2, 103), theta = 51\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 51 * (103 - 51 )/103 =\n", - " = -103 + 102 * (52 )/103 =\n", - " = -103 + 102 * 52/103 = \n", - " = -103 + 5304/103 = \n", - " = -5305/103 \n", - "Pattern part = 5305/103 ~ 51\n", - "Satellite part = 0\n", - "Sigma = 5305/103 ~ 51\n", - "\n", - "3. T(2, 13; 2, 103), theta = 1\n", - "Pattern part = pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = -10405/103 ~ -101\n", - "Satellite part = 0\n", - "Sigma = -10405/103 ~ -101\n", - "\n", - "4. -T(2, 17; 2, 103), theta = 1\n", - "Pattern part = -pp\n", - "pp = -q + 2 * theta * (q - theta)/q =\n", - " = -103 + 2 * 1 * (103 - 1 )/103 =\n", - " = -103 + 2 * (102 )/103 =\n", - " = -103 + 2 * 102/103 = \n", - " = -103 + 204/103 = \n", - " = -10405/103 \n", - "Pattern part = 10405/103 ~ 101\n", - "Satellite part = 0\n", - "Sigma = 10405/103 ~ 101\n", - "\n", - "sigma is big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n" - ] - } - ], - "source": [ - "m.cable_loop_with_details()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0, 11, 0, 83, 0, 17, 13, 103]\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 0, 1, 1] 0\n", - "[0, 0, 2, 2] 0\n", - "[0, 0, 3, 3] 0\n", - "[0, 0, 4, 4] 4\n", - "[0, 0, 5, 5] 4\n", - "[0, 0, 6, 6] 4\n", - "[0, 0, 7, 7] 4\n", - "[0, 0, 8, 8] 4\n", - "[0, 0, 9, 9] 4\n", - "[0, 0, 10, 10] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 1, 1, 0] 0\n", - "[0, 2, 2, 0] 0\n", - "[0, 3, 3, 0] 0\n", - "[0, 4, 4, 0] 4\n", - "[0, 5, 5, 0] 4\n", - "[0, 6, 6, 0] 4\n", - "[0, 7, 7, 0] 4\n", - "[0, 8, 8, 0] 4\n", - "[0, 9, 9, 0] 4\n", - "[0, 10, 10, 0] 4\n", - "[0, 11, 11, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 2, 2, 0] 0\n", - "[0, 4, 4, 0] 4\n", - "[0, 6, 6, 0] 4\n", - "[0, 8, 8, 0] 4\n", - "[0, 10, 10, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 3, 3, 0] 0\n", - "[0, 6, 6, 0] 4\n", - "[0, 9, 9, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 3, 33, 1] 115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 4, 4, 0] 4\n", - "[0, 8, 8, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 4, 10, 1] 95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 5, 5, 0] 4\n", - "[0, 10, 10, 0] 4\n", - "[0, 15, 15, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 5, 21, 1] 107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 6, 6, 0] 4\n", - "[0, 12, 12, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 6, 28, 1] 111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 7, 7, 0] 4\n", - "[0, 14, 14, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 8, 8, 0] 4\n", - "[0, 16, 16, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 8, 27, 1] 107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 9, 9, 0] 4\n", - "[0, 18, 18, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 10, 10, 0] 4\n", - "[0, 20, 20, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 11, 11, 0] 4\n", - "[0, 22, 22, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 12, 12, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 13, 2, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 13, 13, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 14, 14, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 14, 23, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 15, 15, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 16, 16, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 17, 17, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 17, 37, 1] 103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 18, 18, 0] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 19, 14, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 19, 19, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 20, 20, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 20, 22, 1] 95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 21, 21, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 21, 39, 1] 103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 22, 22, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 22, 30, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 23, 23, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 24, 24, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 25, 25, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 26, 26, 0] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 27, 27, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 28, 11, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 28, 28, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 29, 26, 1] 95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 29, 29, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 30, 30, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 31, 7, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 31, 31, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 32, 19, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 32, 32, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 33, 29, 1] 95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 33, 33, 0] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 34, 24, 1] 95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 34, 34, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 35, 8, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 35, 35, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 36, 36, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 37, 37, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 38, 38, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 39, 32, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 39, 39, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 40, 40, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[0, 41, 41, 0] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 0, 0, 1] 0\n", - "[2, 0, 0, 2] 0\n", - "[3, 0, 0, 3] -4\n", - "[4, 0, 0, 4] 0\n", - "[5, 0, 0, 5] 0\n", - "[6, 0, 0, 6] 0\n", - "[7, 0, 0, 7] 0\n", - "[8, 0, 0, 8] -4\n", - "[9, 0, 0, 9] -4\n", - "[10, 0, 0, 10] 0\n", - "[11, 0, 0, 11] 0\n", - "[12, 0, 0, 12] 0\n", - "[13, 0, 0, 13] -4\n", - "[14, 0, 0, 14] -4\n", - "[15, 0, 0, 15] -4\n", - "[16, 0, 0, 16] 0\n", - "[17, 0, 0, 17] 0\n", - "[18, 0, 0, 18] -4\n", - "[19, 0, 0, 19] -4\n", - "[20, 0, 0, 20] -4\n", - "[21, 0, 0, 21] -4\n", - "[22, 0, 0, 22] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 1, 0, 0] 0\n", - "[2, 2, 0, 0] 0\n", - "[3, 3, 0, 0] -4\n", - "[4, 4, 0, 0] 0\n", - "[5, 5, 0, 0] 0\n", - "[6, 6, 0, 0] 0\n", - "[7, 7, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[9, 9, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[11, 11, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[13, 13, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[15, 15, 0, 0] -4\n", - "[16, 16, 0, 0] -4\n", - "[17, 17, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 1, 1, 1] 0\n", - "[2, 2, 2, 2] 0\n", - "[3, 3, 3, 3] -4\n", - "[4, 4, 4, 4] 4\n", - "[5, 5, 5, 5] 4\n", - "[6, 6, 6, 6] 4\n", - "[7, 7, 7, 7] 4\n", - "[8, 8, 8, 8] 0\n", - "[9, 9, 9, 9] 0\n", - "[10, 10, 10, 10] 4\n", - "[11, 11, 11, 11] 4\n", - "[12, 12, 12, 12] 8\n", - "[13, 13, 13, 13] 4\n", - "[14, 14, 14, 14] 4\n", - "[15, 15, 15, 15] 4\n", - "[16, 16, 16, 16] 8\n", - "[17, 17, 17, 17] 8\n", - "[18, 18, 18, 18] 4\n", - "[19, 19, 19, 19] 8\n", - "[20, 20, 20, 20] 8\n", - "[21, 21, 21, 21] 8\n", - "[22, 22, 22, 22] 4\n", - "[23, 23, 23, 23] 8\n", - "[24, 24, 24, 24] 8\n", - "[25, 25, 25, 25] 8\n", - "[26, 26, 26, 26] 8\n", - "[27, 27, 27, 27] 8\n", - "[28, 28, 28, 28] 8\n", - "[29, 29, 29, 29] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 2, 2, 1] 0\n", - "[2, 4, 4, 2] 4\n", - "[3, 6, 6, 3] 0\n", - "[4, 8, 8, 4] 4\n", - "[5, 10, 10, 5] 4\n", - "[6, 12, 12, 6] 8\n", - "[7, 14, 14, 7] 8\n", - "[8, 16, 16, 8] 4\n", - "[9, 18, 18, 9] 4\n", - "[10, 20, 20, 10] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 2, 13, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 3, 3, 1] 0\n", - "[2, 6, 6, 2] 4\n", - "[3, 9, 9, 3] 0\n", - "[4, 12, 12, 4] 8\n", - "[5, 15, 15, 5] 8\n", - "[6, 18, 18, 6] 8\n", - "[7, 21, 21, 7] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 4, 4, 1] 4\n", - "[2, 8, 8, 2] 4\n", - "[3, 12, 12, 3] 4\n", - "[4, 16, 16, 4] 8\n", - "[5, 20, 20, 5] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 5, 5, 1] 4\n", - "[2, 10, 10, 2] 4\n", - "[3, 15, 15, 3] 4\n", - "[4, 20, 20, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 6, 6, 1] 4\n", - "[2, 12, 12, 2] 8\n", - "[3, 18, 18, 3] 4\n", - "[4, 24, 24, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 7, 7, 1] 4\n", - "[2, 14, 14, 2] 8\n", - "[3, 21, 21, 3] 8\n", - "[4, 28, 28, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 7, 31, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 8, 8, 1] 4\n", - "[2, 16, 16, 2] 8\n", - "[3, 24, 24, 3] 8\n", - "[4, 32, 32, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 8, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 9, 9, 1] 4\n", - "[2, 18, 18, 2] 8\n", - "[3, 27, 27, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 10, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 10, 10, 1] 4\n", - "[2, 20, 20, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 11, 11, 1] 4\n", - "[2, 22, 22, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 11, 28, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 12, 12, 1] 8\n", - "[2, 24, 24, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 13, 13, 1] 8\n", - "[2, 26, 26, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 14, 14, 1] 8\n", - "[2, 28, 28, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 14, 19, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 15, 15, 1] 8\n", - "[2, 30, 30, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 16, 16, 1] 8\n", - "[2, 32, 32, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 17, 17, 1] 8\n", - "[2, 34, 34, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 18, 18, 1] 8\n", - "[2, 36, 36, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 19, 19, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 19, 32, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 20, 20, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 21, 5, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 21, 21, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 22, 20, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 22, 22, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 23, 14, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 23, 23, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 24, 24, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 24, 34, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 25, 25, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 26, 26, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 26, 29, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 27, 8, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 27, 27, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 28, 6, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 28, 28, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 29, 29, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 29, 33, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 30, 22, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 30, 30, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 31, 31, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 32, 32, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 32, 39, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 33, 3, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 33, 33, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 34, 34, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 35, 35, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 36, 36, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 37, 17, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 37, 37, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 38, 38, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 39, 21, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 39, 39, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 40, 40, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[1, 41, 41, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 1, 9, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 2, 0, 0] 0\n", - "[4, 4, 0, 0] 0\n", - "[6, 6, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[14, 14, 0, 0] -4\n", - "[16, 16, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 2, 1, 1] 0\n", - "[4, 4, 2, 2] 0\n", - "[6, 6, 3, 3] 0\n", - "[8, 8, 4, 4] 0\n", - "[10, 10, 5, 5] 0\n", - "[12, 12, 6, 6] 4\n", - "[14, 14, 7, 7] 0\n", - "[16, 16, 8, 8] 0\n", - "[18, 18, 9, 9] -4\n", - "[20, 20, 10, 10] 4\n", - "[22, 22, 11, 11] 0\n", - "[24, 24, 12, 12] 0\n", - "[26, 26, 13, 13] 0\n", - "[28, 28, 14, 14] 0\n", - "[30, 30, 15, 15] 0\n", - "[32, 32, 16, 16] 0\n", - "[34, 34, 17, 17] 4\n", - "[36, 36, 18, 18] 4\n", - "[38, 38, 19, 19] 0\n", - "[40, 40, 20, 20] 0\n", - "[42, 42, 21, 21] 0\n", - "[44, 44, 22, 22] 0\n", - "[46, 46, 23, 23] 4\n", - "[48, 48, 24, 24] 8\n", - "[50, 50, 25, 25] 4\n", - "[52, 52, 26, 26] 8\n", - "[54, 54, 27, 27] 8\n", - "[56, 56, 28, 28] 8\n", - "[58, 58, 29, 29] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 4, 26, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 5, 41, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 6, 38, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 8, 12, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 9, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 9, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 13, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 14, 21, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 14, 39, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 16, 2, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 16, 13, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 17, 6, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 17, 28, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 19, 5, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 19, 21, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 20, 8, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 20, 27, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 21, 40, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 22, 27, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 23, 32, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 23, 39, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 24, 18, 1] 8\n", - "[4, 48, 36, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 25, 17, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 25, 37, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 26, 3, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 27, 12, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 28, 38, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 29, 16, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 31, 25, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 32, 5, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 33, 16, 1] 4\n", - "[4, 66, 32, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 35, 15, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 36, 31, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 37, 11, 1] 0\n", - "[4, 74, 22, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 37, 28, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 38, 14, 1] 4\n", - "[4, 76, 28, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 38, 19, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 39, 40, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[2, 41, 10, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 0, 18, 1] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 1, 18, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 2, 24, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 3, 0, 0] -4\n", - "[6, 6, 0, 0] 0\n", - "[9, 9, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[15, 15, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 3, 1, 1] -4\n", - "[6, 6, 2, 2] 0\n", - "[9, 9, 3, 3] -4\n", - "[12, 12, 4, 4] 4\n", - "[15, 15, 5, 5] 0\n", - "[18, 18, 6, 6] -4\n", - "[21, 21, 7, 7] 0\n", - "[24, 24, 8, 8] -4\n", - "[27, 27, 9, 9] -4\n", - "[30, 30, 10, 10] 0\n", - "[33, 33, 11, 11] -4\n", - "[36, 36, 12, 12] 0\n", - "[39, 39, 13, 13] -4\n", - "[42, 42, 14, 14] -4\n", - "[45, 45, 15, 15] -4\n", - "[48, 48, 16, 16] 4\n", - "[51, 51, 17, 17] 0\n", - "[54, 54, 18, 18] 4\n", - "[57, 57, 19, 19] 4\n", - "[60, 60, 20, 20] 4\n", - "[63, 63, 21, 21] 8\n", - "[66, 66, 22, 22] 8\n", - "[69, 69, 23, 23] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 4, 16, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 5, 4, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 5, 10, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 6, 32, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 6, 39, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 7, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 7, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 10, 3, 1] -8\n", - "[6, 20, 6, 2] -4\n", - "[9, 30, 9, 3] -4\n", - "[12, 40, 12, 4] 8\n", - "[15, 50, 15, 5] 8\n", - "[18, 60, 18, 6] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 11, 14, 1] 8\n", - "[6, 22, 28, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 11, 19, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 13, 24, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 13, 34, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 14, 41, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 15, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 16, 9, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 17, 23, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 19, 41, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 20, 15, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 21, 10, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 22, 12, 1] 0\n", - "[6, 44, 24, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[3, 23, 40, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 24, 22, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 24, 30, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 25, 6, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 26, 2, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 26, 13, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 28, 19, 1] 8\n", - "[6, 56, 38, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 28, 32, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 29, 13, 1] 0\n", - "[6, 58, 26, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 30, 12, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 31, 17, 1] 4\n", - "[6, 62, 34, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 33, 1, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 34, 20, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 34, 22, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 37, 38, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 38, 5, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[3, 41, 26, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 0, 20, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 1, 20, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 1, 22, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 3, 34, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 4, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[12, 12, 0, 0] 0\n", - "[16, 16, 0, 0] -4\n", - "[20, 20, 0, 0] -4\n", - "[24, 24, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 4, 1, 1] 0\n", - "[8, 8, 2, 2] -4\n", - "[12, 12, 3, 3] 0\n", - "[16, 16, 4, 4] 0\n", - "[20, 20, 5, 5] 0\n", - "[24, 24, 6, 6] -4\n", - "[28, 28, 7, 7] -4\n", - "[32, 32, 8, 8] -8\n", - "[36, 36, 9, 9] -4\n", - "[40, 40, 10, 10] -4\n", - "[44, 44, 11, 11] -4\n", - "[48, 48, 12, 12] 0\n", - "[52, 52, 13, 13] 0\n", - "[56, 56, 14, 14] 0\n", - "[60, 60, 15, 15] 0\n", - "[64, 64, 16, 16] 8\n", - "[68, 68, 17, 17] 8\n", - "[72, 72, 18, 18] 8\n", - "[76, 76, 19, 19] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 5, 3, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 5, 33, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 6, 41, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 7, 38, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 8, 7, 1] 4\n", - "[8, 16, 14, 2] 8\n", - "[12, 24, 21, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 8, 31, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 9, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 10, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 11, 40, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 13, 30, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 15, 25, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 16, 18, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 17, 5, 1] -8\n", - "[8, 34, 10, 2] 0\n", - "[12, 51, 15, 3] 8\n", - "[16, 68, 20, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 18, 15, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 21, 29, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 21, 33, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 23, 4, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 24, 35, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 25, 19, 1] 8\n", - "[8, 50, 38, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 25, 32, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 27, 7, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 28, 41, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 29, 24, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 31, 38, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 32, 26, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 33, 24, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 33, 34, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 34, 12, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 35, 31, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 36, 6, 1] -8\n", - "[8, 72, 12, 2] 8\n", - "[12, 108, 18, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 37, 5, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 37, 21, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 38, 10, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 39, 26, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 39, 29, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[4, 40, 16, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 0, 15, 1] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 1, 15, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 2, 35, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 3, 20, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 4, 18, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 5, 0, 0] 0\n", - "[10, 10, 0, 0] -4\n", - "[15, 15, 0, 0] -4\n", - "[20, 20, 0, 0] -4\n", - "[25, 25, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 5, 1, 1] 0\n", - "[10, 10, 2, 2] -4\n", - "[15, 15, 3, 3] -4\n", - "[20, 20, 4, 4] 0\n", - "[25, 25, 5, 5] -4\n", - "[30, 30, 6, 6] -4\n", - "[35, 35, 7, 7] -4\n", - "[40, 40, 8, 8] -8\n", - "[45, 45, 9, 9] -8\n", - "[50, 50, 10, 10] -4\n", - "[55, 55, 11, 11] 0\n", - "[60, 60, 12, 12] 0\n", - "[65, 65, 13, 13] 0\n", - "[70, 70, 14, 14] 4\n", - "[75, 75, 15, 15] 4\n", - "[80, 80, 16, 16] 8\n", - "[85, 85, 17, 17] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 6, 26, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 6, 29, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 7, 5, 1] 4\n", - "[10, 14, 10, 2] 8\n", - "[15, 21, 15, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 8, 17, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 10, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 12, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 12, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 13, 12, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 16, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 17, 4, 1] -8\n", - "[10, 34, 8, 2] 0\n", - "[15, 51, 12, 3] 4\n", - "[20, 68, 16, 4] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 18, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 19, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 20, 25, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 21, 1, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 22, 25, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 23, 16, 1] 8\n", - "[10, 46, 32, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 26, 30, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 27, 17, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 27, 37, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 28, 26, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 29, 22, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 29, 30, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 31, 40, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 32, 2, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 32, 13, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 33, 20, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 33, 22, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 35, 11, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 36, 21, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 36, 39, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 37, 4, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 37, 10, 1] 0\n", - "[10, 74, 20, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 38, 3, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 39, 13, 1] 4\n", - "[10, 78, 26, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[5, 40, 9, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 0, 31, 1] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 1, 7, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 1, 31, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 2, 36, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 4, 8, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 4, 35, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 6, 0, 0] 0\n", - "[12, 12, 0, 0] 0\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 6, 1, 1] 0\n", - "[12, 12, 2, 2] 0\n", - "[18, 18, 3, 3] -8\n", - "[24, 24, 4, 4] -4\n", - "[30, 30, 5, 5] -4\n", - "[36, 36, 6, 6] -4\n", - "[42, 42, 7, 7] -8\n", - "[48, 48, 8, 8] -4\n", - "[54, 54, 9, 9] -4\n", - "[60, 60, 10, 10] 0\n", - "[66, 66, 11, 11] 4\n", - "[72, 72, 12, 12] 4\n", - "[78, 78, 13, 13] 8\n", - "[84, 84, 14, 14] 8\n", - "[90, 90, 15, 15] 8\n", - "[96, 96, 16, 16] 8\n", - "[102, 102, 17, 17] 8\n", - "[108, 108, 18, 18] 4\n", - "[114, 114, 19, 19] 4\n", - "[120, 120, 20, 20] 0\n", - "[126, 126, 21, 21] 0\n", - "[132, 132, 22, 22] 4\n", - "[138, 138, 23, 23] 8\n", - "[144, 144, 24, 24] 8\n", - "[150, 150, 25, 25] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 8, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 8, 32, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 10, 8, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 10, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 11, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 12, 5, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 12, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 13, 36, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 14, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 14, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 15, 40, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 17, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 18, 17, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 19, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 20, 38, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 22, 38, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 23, 24, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 25, 3, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 26, 15, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 27, 14, 1] 8\n", - "[12, 54, 28, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 27, 19, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 28, 1, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 29, 15, 1] 8\n", - "[12, 58, 30, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 31, 26, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 32, 18, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 34, 37, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 35, 32, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 35, 39, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 36, 4, 1] -8\n", - "[12, 72, 8, 2] 8\n", - "[18, 108, 12, 3] 4\n", - "[24, 144, 16, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 38, 9, 1] 0\n", - "[12, 76, 18, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 39, 18, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 40, 30, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 41, 20, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[6, 41, 22, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 1, 6, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 2, 11, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 3, 25, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 4, 36, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 5, 15, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 6, 30, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 7, 0, 0] 0\n", - "[14, 14, 0, 0] -4\n", - "[21, 21, 0, 0] -4\n", - "[28, 28, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 7, 1, 1] 0\n", - "[14, 14, 2, 2] -4\n", - "[21, 21, 3, 3] -4\n", - "[28, 28, 4, 4] -4\n", - "[35, 35, 5, 5] -4\n", - "[42, 42, 6, 6] -8\n", - "[49, 49, 7, 7] -4\n", - "[56, 56, 8, 8] -4\n", - "[63, 63, 9, 9] 0\n", - "[70, 70, 10, 10] 4\n", - "[77, 77, 11, 11] 8\n", - "[84, 84, 12, 12] 8\n", - "[91, 91, 13, 13] 4\n", - "[98, 98, 14, 14] 4\n", - "[105, 105, 15, 15] 0\n", - "[112, 112, 16, 16] 4\n", - "[119, 119, 17, 17] 4\n", - "[126, 126, 18, 18] 0\n", - "[133, 133, 19, 19] 0\n", - "[140, 140, 20, 20] 4\n", - "[147, 147, 21, 21] 8\n", - "[154, 154, 22, 22] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 8, 4, 1] 4\n", - "[14, 16, 8, 2] 4\n", - "[21, 24, 12, 3] 8\n", - "[28, 32, 16, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 9, 38, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 10, 36, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 12, 26, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 13, 11, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 13, 28, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 14, 8, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 14, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 15, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 15, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 16, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 17, 18, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 18, 21, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 18, 39, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 19, 8, 1] 4\n", - "[14, 38, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 19, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 21, 12, 1] 8\n", - "[14, 42, 24, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 22, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 23, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 24, 14, 1] 8\n", - "[14, 48, 28, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 24, 19, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 25, 24, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 27, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 27, 10, 1] 4\n", - "[14, 54, 20, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 30, 41, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 31, 0, 1] 67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 32, 35, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 33, 25, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 34, 19, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 34, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 36, 13, 1] 8\n", - "[14, 72, 26, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 37, 18, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 38, 20, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[7, 39, 12, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 1, 41, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 2, 40, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 3, 19, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 3, 32, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 4, 6, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 5, 25, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 7, 20, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 7, 22, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 8, 0, 0] -4\n", - "[16, 16, 0, 0] -4\n", - "[24, 24, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 8, 1, 1] -4\n", - "[16, 16, 2, 2] -4\n", - "[24, 24, 3, 3] -8\n", - "[32, 32, 4, 4] -8\n", - "[40, 40, 5, 5] -8\n", - "[48, 48, 6, 6] -4\n", - "[56, 56, 7, 7] -4\n", - "[64, 64, 8, 8] 0\n", - "[72, 72, 9, 9] 0\n", - "[80, 80, 10, 10] 4\n", - "[88, 88, 11, 11] 8\n", - "[96, 96, 12, 12] 4\n", - "[104, 104, 13, 13] 4\n", - "[112, 112, 14, 14] 0\n", - "[120, 120, 15, 15] -4\n", - "[128, 128, 16, 16] 0\n", - "[136, 136, 17, 17] 4\n", - "[144, 144, 18, 18] 4\n", - "[152, 152, 19, 19] 8\n", - "[160, 160, 20, 20] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 9, 10, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 10, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 10, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 12, 9, 1] 8\n", - "[16, 24, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 13, 40, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 14, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 15, 24, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 16, 21, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 16, 39, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 17, 15, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 18, 26, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 18, 29, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 19, 7, 1] 0\n", - "[16, 38, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 19, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 20, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 23, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 25, 8, 1] -4\n", - "[16, 50, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 25, 35, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 26, 23, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 27, 1, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 29, 14, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 29, 23, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 30, 16, 1] 8\n", - "[16, 60, 32, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 31, 20, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 32, 31, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 33, 14, 1] 4\n", - "[16, 66, 28, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 33, 19, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 35, 0, 1] 67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 36, 30, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 37, 12, 1] 4\n", - "[16, 74, 24, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 41, 17, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[8, 41, 37, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 0, 13, 1] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 1, 2, 1] 8\n", - "[18, 2, 4, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 1, 13, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 2, 16, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 3, 26, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 3, 29, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 5, 32, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 5, 39, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 6, 11, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 7, 36, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 9, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 9, 1, 1] -4\n", - "[18, 18, 2, 2] -8\n", - "[27, 27, 3, 3] -8\n", - "[36, 36, 4, 4] -4\n", - "[45, 45, 5, 5] -8\n", - "[54, 54, 6, 6] -4\n", - "[63, 63, 7, 7] 0\n", - "[72, 72, 8, 8] 0\n", - "[81, 81, 9, 9] 4\n", - "[90, 90, 10, 10] 8\n", - "[99, 99, 11, 11] 4\n", - "[108, 108, 12, 12] 0\n", - "[117, 117, 13, 13] 0\n", - "[126, 126, 14, 14] -4\n", - "[135, 135, 15, 15] 0\n", - "[144, 144, 16, 16] 4\n", - "[153, 153, 17, 17] 8\n", - "[162, 162, 18, 18] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 11, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 11, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 12, 8, 1] 8\n", - "[18, 24, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 12, 35, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 14, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 15, 12, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 16, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 16, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 18, 24, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 18, 34, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 19, 23, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 20, 30, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 21, 19, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 21, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 23, 38, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 24, 9, 1] 0\n", - "[18, 48, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 27, 20, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 28, 17, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 31, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 32, 14, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 32, 23, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 33, 26, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 35, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 37, 25, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 38, 6, 1] -4\n", - "[18, 76, 12, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 39, 14, 1] 8\n", - "[18, 78, 28, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 39, 19, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 40, 5, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 40, 21, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[9, 41, 40, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 1, 20, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 2, 30, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 3, 18, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 4, 0, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 5, 3, 1] 8\n", - "[20, 10, 6, 2] 8\n", - "[30, 15, 9, 3] 8\n", - "[40, 20, 12, 4] 8\n", - "[50, 25, 15, 5] 8\n", - "[60, 30, 18, 6] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 7, 38, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 8, 31, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 9, 8, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 9, 27, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 10, 0, 0] -4\n", - "[20, 20, 0, 0] -4\n", - "[30, 30, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 10, 1, 1] -4\n", - "[20, 20, 2, 2] -4\n", - "[30, 30, 3, 3] -8\n", - "[40, 40, 4, 4] -8\n", - "[50, 50, 5, 5] -8\n", - "[60, 60, 6, 6] -4\n", - "[70, 70, 7, 7] 0\n", - "[80, 80, 8, 8] 0\n", - "[90, 90, 9, 9] 4\n", - "[100, 100, 10, 10] 4\n", - "[110, 110, 11, 11] 0\n", - "[120, 120, 12, 12] -4\n", - "[130, 130, 13, 13] 0\n", - "[140, 140, 14, 14] 0\n", - "[150, 150, 15, 15] 4\n", - "[160, 160, 16, 16] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 11, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 12, 25, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 13, 22, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 13, 30, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 17, 40, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 18, 15, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 19, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 20, 36, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 21, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 21, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 24, 12, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 25, 32, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 25, 39, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 26, 24, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 27, 7, 1] 0\n", - "[20, 54, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 27, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 28, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 29, 24, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 29, 34, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 31, 23, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 32, 26, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 32, 29, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 33, 34, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 34, 12, 1] 8\n", - "[20, 68, 24, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 37, 5, 1] -4\n", - "[20, 74, 10, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 38, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 38, 10, 1] 4\n", - "[20, 76, 20, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 39, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 39, 33, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 40, 16, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[10, 41, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 2, 7, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 4, 12, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 5, 30, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 6, 9, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 7, 26, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 7, 29, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 8, 21, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 8, 39, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 9, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 10, 35, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 11, 0, 0] -4\n", - "[22, 22, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 11, 1, 1] -4\n", - "[22, 22, 2, 2] -8\n", - "[33, 33, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 12, 40, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 13, 7, 1] 8\n", - "[22, 26, 14, 2] 8\n", - "[33, 39, 21, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 13, 31, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 14, 18, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 15, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 17, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 18, 11, 1] 8\n", - "[22, 36, 22, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 18, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 19, 18, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 20, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 20, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 22, 23, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 23, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 24, 17, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 24, 37, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 25, 16, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 27, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 27, 39, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 28, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 30, 38, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 31, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 31, 33, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 34, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 35, 5, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 35, 21, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 37, 2, 1] -8\n", - "[22, 74, 4, 2] 4\n", - "[33, 111, 6, 3] -4\n", - "[44, 148, 8, 4] 0\n", - "[55, 185, 10, 5] 8\n", - "[66, 222, 12, 6] 8\n", - "[77, 259, 14, 7] 8\n", - "[88, 296, 16, 8] 0\n", - "[99, 333, 18, 9] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 37, 13, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 38, 24, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 40, 20, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[11, 40, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 0, 40, 1] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 1, 40, 0] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 2, 21, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 2, 39, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 3, 23, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 4, 11, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 5, 31, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 6, 15, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 8, 2, 1] 4\n", - "[24, 16, 4, 2] 0\n", - "[36, 24, 6, 3] -4\n", - "[48, 32, 8, 4] 0\n", - "[60, 40, 10, 5] 4\n", - "[72, 48, 12, 6] 4\n", - "[84, 56, 14, 7] -4\n", - "[96, 64, 16, 8] 8\n", - "[108, 72, 18, 9] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 8, 13, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 9, 41, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 10, 17, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 11, 12, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 12, 0, 0] 0\n", - "[24, 24, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 12, 1, 1] 0\n", - "[24, 24, 2, 2] -8\n", - "[36, 36, 3, 3] -8\n", - "[48, 48, 4, 4] -4\n", - "[60, 60, 5, 5] -4\n", - "[72, 72, 6, 6] 0\n", - "[84, 84, 7, 7] 4\n", - "[96, 96, 8, 8] 0\n", - "[108, 108, 9, 9] -4\n", - "[120, 120, 10, 10] -4\n", - "[132, 132, 11, 11] 0\n", - "[144, 144, 12, 12] 0\n", - "[156, 156, 13, 13] 4\n", - "[168, 168, 14, 14] 8\n", - "[180, 180, 15, 15] 4\n", - "[192, 192, 16, 16] 4\n", - "[204, 204, 17, 17] 0\n", - "[216, 216, 18, 18] 0\n", - "[228, 228, 19, 19] 8\n", - "[240, 240, 20, 20] 8\n", - "[252, 252, 21, 21] 8\n", - "[264, 264, 22, 22] 8\n", - "[276, 276, 23, 23] 8\n", - "[288, 288, 24, 24] 4\n", - "[300, 300, 25, 25] 4\n", - "[312, 312, 26, 26] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 13, 5, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 13, 21, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 15, 9, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 16, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 16, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 17, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 19, 36, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 20, 16, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 21, 7, 1] 4\n", - "[24, 42, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 21, 31, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 22, 3, 1] -4\n", - "[24, 44, 6, 2] 0\n", - "[36, 66, 9, 3] 4\n", - "[48, 88, 12, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 24, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 27, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 28, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 29, 38, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 30, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 30, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 31, 30, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 32, 36, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 33, 38, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 34, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 34, 10, 1] 8\n", - "[24, 68, 20, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 35, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 37, 8, 1] 4\n", - "[24, 74, 16, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 37, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 39, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[12, 41, 25, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 0, 9, 1] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 1, 9, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 2, 1, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 3, 16, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 5, 40, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 6, 38, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 8, 12, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 9, 24, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 11, 6, 1] 4\n", - "[26, 22, 12, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 12, 15, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 13, 0, 0] -4\n", - "[26, 26, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 13, 1, 1] -4\n", - "[26, 26, 2, 2] -8\n", - "[39, 39, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 14, 32, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 14, 39, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 16, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 17, 11, 1] 8\n", - "[26, 34, 22, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 17, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 19, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 19, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 20, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 21, 40, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 23, 19, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 23, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 24, 18, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 25, 37, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 26, 3, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 26, 33, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 27, 35, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 29, 3, 1] -8\n", - "[26, 58, 6, 2] 0\n", - "[39, 87, 9, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 30, 20, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 32, 5, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 32, 21, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 33, 16, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 34, 18, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 35, 12, 1] 8\n", - "[26, 70, 24, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 36, 7, 1] 0\n", - "[26, 72, 14, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 36, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 37, 11, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 38, 14, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 38, 23, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 39, 5, 1] -4\n", - "[26, 78, 10, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[13, 40, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 3, 35, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 4, 22, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 4, 30, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 5, 24, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 6, 16, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 9, 36, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 10, 30, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 11, 3, 1] 0\n", - "[28, 22, 6, 2] 0\n", - "[42, 33, 9, 3] -4\n", - "[56, 44, 12, 4] 8\n", - "[70, 55, 15, 5] 8\n", - "[84, 66, 18, 6] 4\n", - "[98, 77, 21, 7] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 12, 23, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 14, 0, 0] -4\n", - "[28, 28, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 14, 1, 1] -4\n", - "[28, 28, 2, 2] -8\n", - "[42, 42, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 15, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 15, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 16, 12, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 17, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 17, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 19, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 20, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 22, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 23, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 24, 7, 1] 0\n", - "[28, 48, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 24, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 26, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 27, 6, 1] 0\n", - "[28, 54, 12, 2] 8\n", - "[42, 81, 18, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 28, 16, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 29, 8, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 29, 27, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 30, 17, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 30, 37, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 32, 9, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 33, 8, 1] 0\n", - "[28, 66, 16, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 33, 35, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 34, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 35, 38, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 36, 41, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 37, 26, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 37, 29, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 38, 2, 1] -8\n", - "[28, 76, 4, 2] 8\n", - "[42, 114, 6, 3] -8\n", - "[56, 152, 8, 4] 8\n", - "[70, 190, 10, 5] 0\n", - "[84, 228, 12, 6] -4\n", - "[98, 266, 14, 7] 8\n", - "[112, 304, 16, 8] 8\n", - "[126, 342, 18, 9] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 38, 13, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 39, 9, 1] 4\n", - "[28, 78, 18, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 40, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[14, 41, 18, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 0, 5, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 1, 5, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 1, 21, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 2, 19, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 2, 32, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 3, 38, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 4, 17, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 4, 37, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 5, 7, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 6, 12, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 9, 40, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 10, 37, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 11, 35, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 12, 13, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 13, 32, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 13, 39, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 15, 0, 0] -4\n", - "[30, 30, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 15, 1, 1] -4\n", - "[30, 30, 2, 2] -8\n", - "[45, 45, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 16, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 17, 8, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 17, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 18, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 18, 10, 1] 8\n", - "[30, 36, 20, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 20, 3, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 20, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 21, 36, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 22, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 22, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 25, 20, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 25, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 26, 6, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 26, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 27, 16, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 28, 12, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 29, 6, 1] 0\n", - "[30, 58, 12, 2] 8\n", - "[45, 87, 18, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 30, 26, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 30, 29, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 35, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 36, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 37, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 39, 36, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[15, 40, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 0, 34, 1] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 1, 24, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 1, 34, 0] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 2, 9, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 3, 13, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 4, 3, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 4, 33, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 6, 14, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 6, 19, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 9, 18, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 10, 29, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 10, 33, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 11, 23, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 14, 40, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 16, 0, 0] -4\n", - "[32, 32, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 16, 1, 1] -4\n", - "[32, 32, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 17, 38, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 18, 20, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 18, 22, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 19, 40, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 20, 12, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 22, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 23, 5, 1] 0\n", - "[32, 46, 10, 2] 4\n", - "[48, 69, 15, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 25, 11, 1] 8\n", - "[32, 50, 22, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 25, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 27, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 28, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 28, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 29, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 30, 8, 1] 4\n", - "[32, 60, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 30, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 31, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 32, 41, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 33, 2, 1] -8\n", - "[32, 66, 4, 2] -4\n", - "[48, 99, 6, 3] 0\n", - "[64, 132, 8, 4] 4\n", - "[80, 165, 10, 5] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 33, 13, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 34, 30, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 36, 25, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 38, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 38, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 39, 41, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 40, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[16, 40, 10, 1] 8\n", - "[32, 80, 20, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 0, 25, 1] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 1, 25, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 2, 31, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 4, 15, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 5, 20, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 5, 22, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 7, 3, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 7, 33, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 8, 5, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 9, 37, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 10, 12, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 11, 9, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 12, 41, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 16, 36, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 17, 0, 0] -4\n", - "[34, 34, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 17, 1, 1] -4\n", - "[34, 34, 2, 2] -8\n", - "[51, 51, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 18, 6, 1] 4\n", - "[34, 36, 12, 2] 8\n", - "[51, 54, 18, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 20, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 20, 32, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 21, 22, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 21, 30, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 22, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 22, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 23, 18, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 24, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 25, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 27, 5, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 27, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 28, 9, 1] 8\n", - "[34, 56, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 30, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 30, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 31, 3, 1] -4\n", - "[34, 62, 6, 2] 0\n", - "[51, 93, 9, 3] 8\n", - "[68, 124, 12, 4] 8\n", - "[85, 155, 15, 5] 8\n", - "[102, 186, 18, 6] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 34, 11, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 34, 28, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 35, 40, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 36, 26, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 36, 29, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 37, 1, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 38, 34, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 39, 30, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 41, 8, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[17, 41, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 0, 3, 1] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 1, 3, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 1, 33, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 2, 26, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 3, 10, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 4, 5, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 5, 38, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 6, 25, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 9, 16, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 10, 5, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 10, 21, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 12, 22, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 12, 30, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 13, 26, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 13, 29, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 14, 11, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 15, 20, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 16, 4, 1] 0\n", - "[36, 32, 8, 2] 0\n", - "[54, 48, 12, 3] 8\n", - "[72, 64, 16, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 17, 7, 1] 4\n", - "[36, 34, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 17, 31, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 18, 1, 1] -8\n", - "[36, 36, 2, 2] -8\n", - "[54, 54, 3, 3] -8\n", - "[72, 72, 4, 4] 0\n", - "[90, 90, 5, 5] 4\n", - "[108, 108, 6, 6] -4\n", - "[126, 126, 7, 7] -8\n", - "[144, 144, 8, 8] -4\n", - "[162, 162, 9, 9] 4\n", - "[180, 180, 10, 10] 4\n", - "[198, 198, 11, 11] -4\n", - "[216, 216, 12, 12] -4\n", - "[234, 234, 13, 13] 4\n", - "[252, 252, 14, 14] 4\n", - "[270, 270, 15, 15] 4\n", - "[288, 288, 16, 16] 0\n", - "[306, 306, 17, 17] 4\n", - "[324, 324, 18, 18] 8\n", - "[342, 342, 19, 19] 8\n", - "[360, 360, 20, 20] 4\n", - "[378, 378, 21, 21] 0\n", - "[396, 396, 22, 22] 8\n", - "[414, 414, 23, 23] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 19, 11, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 19, 28, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 20, 34, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 22, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 22, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 23, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 24, 2, 1] -8\n", - "[36, 48, 4, 2] -4\n", - "[54, 72, 6, 3] 4\n", - "[72, 96, 8, 4] 8\n", - "[90, 120, 10, 5] 0\n", - "[108, 144, 12, 6] 8\n", - "[126, 168, 14, 7] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 24, 13, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 26, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 30, 24, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 32, 6, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 32, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 34, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 36, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 37, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 38, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 39, 6, 1] 0\n", - "[36, 78, 12, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 40, 23, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 41, 14, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[18, 41, 19, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 2, 15, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 3, 8, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 3, 35, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 4, 30, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 6, 16, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 7, 41, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 8, 6, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 11, 3, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 11, 33, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 12, 38, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 14, 1, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 15, 14, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 15, 23, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 16, 12, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 17, 26, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 17, 29, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 19, 0, 0] -4\n", - "[38, 38, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 19, 1, 1] -4\n", - "[38, 38, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 20, 17, 1] 20\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 21, 9, 1] 8\n", - "[38, 42, 18, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 22, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 22, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 23, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 24, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 25, 4, 1] -4\n", - "[38, 50, 8, 2] -4\n", - "[57, 75, 12, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 27, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 27, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 28, 3, 1] -4\n", - "[38, 56, 6, 2] -4\n", - "[57, 84, 9, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 29, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 30, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 32, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 33, 8, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 33, 27, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 34, 7, 1] 4\n", - "[38, 68, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 34, 31, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 36, 40, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 37, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 38, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 39, 9, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 40, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 40, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[19, 41, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 0, 4, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 1, 4, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 1, 10, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 3, 5, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 4, 23, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 5, 17, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 5, 37, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 6, 36, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 7, 8, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 7, 27, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 10, 38, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 12, 34, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 15, 18, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 16, 40, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 18, 16, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 19, 25, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 20, 0, 0] -4\n", - "[40, 40, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 20, 1, 1] -4\n", - "[40, 40, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 21, 37, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 22, 1, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 24, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 24, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 25, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 26, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 26, 39, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 27, 9, 1] 8\n", - "[40, 54, 18, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 29, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 29, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 30, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 31, 8, 1] 4\n", - "[40, 62, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 31, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 32, 25, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 33, 5, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 33, 21, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 34, 3, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 34, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 35, 24, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 38, 7, 1] 4\n", - "[40, 76, 14, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 38, 31, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 40, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 41, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[20, 41, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 1, 15, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 2, 12, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 5, 0, 1] 91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 6, 29, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 6, 33, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 7, 40, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 8, 11, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 10, 18, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 11, 26, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 12, 6, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 13, 12, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 14, 2, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 15, 38, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 16, 8, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 16, 27, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 18, 7, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 19, 2, 1] 0\n", - "[42, 38, 4, 2] -8\n", - "[63, 57, 6, 3] -4\n", - "[84, 76, 8, 4] 4\n", - "[105, 95, 10, 5] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 19, 13, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 21, 0, 0] -4\n", - "[42, 42, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 21, 1, 1] -4\n", - "[42, 42, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 22, 25, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 26, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 26, 30, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 27, 17, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 28, 26, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 28, 29, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 29, 20, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 29, 22, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 30, 25, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 31, 40, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 32, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 33, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 34, 36, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 35, 11, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 35, 28, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 36, 5, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 36, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 37, 4, 1] 0\n", - "[42, 74, 8, 2] 8\n", - "[63, 111, 12, 3] 8\n", - "[84, 148, 16, 4] 4\n", - "[105, 185, 20, 5] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 38, 16, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 39, 1, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 40, 9, 1] 8\n", - "[42, 80, 18, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[21, 41, 24, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 1, 4, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 3, 40, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 4, 14, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 4, 23, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 5, 17, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 6, 36, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 7, 8, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 7, 35, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 8, 24, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 9, 26, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 10, 23, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 12, 18, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 13, 10, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 14, 25, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 16, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 18, 16, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 19, 25, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 20, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 21, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 21, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 22, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 22, 1, 1] -8\n", - "[44, 44, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 24, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 24, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 25, 15, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 26, 21, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 26, 39, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 28, 36, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 29, 5, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 29, 21, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 30, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 31, 35, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 33, 5, 1] -4\n", - "[44, 66, 10, 2] 4\n", - "[66, 99, 15, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 34, 3, 1] -4\n", - "[44, 68, 6, 2] 0\n", - "[66, 102, 9, 3] 8\n", - "[88, 136, 12, 4] 0\n", - "[110, 170, 15, 5] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 35, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 35, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 36, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 38, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 39, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 40, 11, 1] 8\n", - "[44, 80, 22, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 40, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[22, 41, 6, 1] 0\n", - "[44, 82, 12, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 3, 12, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 4, 20, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 4, 22, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 5, 24, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 5, 34, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 8, 38, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 9, 36, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 10, 22, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 10, 30, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 11, 16, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 12, 14, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 12, 23, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 14, 0, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 15, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 15, 32, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 16, 15, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 17, 3, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 17, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 18, 25, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 19, 9, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 20, 11, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 20, 28, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 21, 24, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 22, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 23, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 23, 1, 1] -8\n", - "[46, 46, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 24, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 26, 8, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 26, 27, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 28, 16, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 29, 8, 1] 4\n", - "[46, 58, 16, 2] 8\n", - "[69, 87, 24, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 29, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 30, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 31, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 32, 9, 1] 4\n", - "[46, 64, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 33, 35, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[23, 35, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 36, 41, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 37, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 37, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 38, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[23, 40, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 1, 16, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 2, 3, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 2, 33, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 4, 41, 0] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 5, 14, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 5, 23, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 6, 37, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 8, 22, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 8, 30, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 9, 2, 1] 4\n", - "[48, 18, 4, 2] -4\n", - "[72, 27, 6, 3] -4\n", - "[96, 36, 8, 4] 0\n", - "[120, 45, 10, 5] 0\n", - "[144, 54, 12, 6] 4\n", - "[168, 63, 14, 7] 0\n", - "[192, 72, 16, 8] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 9, 13, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 10, 40, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 11, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 13, 3, 1] 4\n", - "[48, 26, 6, 2] -4\n", - "[72, 39, 9, 3] 0\n", - "[96, 52, 12, 4] 4\n", - "[120, 65, 15, 5] 8\n", - "[144, 78, 18, 6] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 14, 6, 1] 8\n", - "[48, 28, 12, 2] 8\n", - "[72, 42, 18, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 15, 8, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 15, 27, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 16, 26, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 18, 9, 1] 8\n", - "[48, 36, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 21, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 22, 18, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 23, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 23, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 24, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 24, 1, 1] -8\n", - "[48, 48, 2, 2] -8\n", - "[72, 72, 3, 3] -4\n", - "[96, 96, 4, 4] 0\n", - "[120, 120, 5, 5] -8\n", - "[144, 144, 6, 6] -4\n", - "[168, 168, 7, 7] 4\n", - "[192, 192, 8, 8] -4\n", - "[216, 216, 9, 9] -8\n", - "[240, 240, 10, 10] 4\n", - "[264, 264, 11, 11] 4\n", - "[288, 288, 12, 12] -4\n", - "[312, 312, 13, 13] 4\n", - "[336, 336, 14, 14] 8\n", - "[360, 360, 15, 15] 0\n", - "[384, 384, 16, 16] 4\n", - "[408, 408, 17, 17] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 25, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 26, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 27, 30, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 29, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 29, 10, 1] 8\n", - "[48, 58, 20, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 30, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 32, 38, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 33, 4, 1] -4\n", - "[48, 66, 8, 2] 4\n", - "[72, 99, 12, 3] 8\n", - "[96, 132, 16, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 34, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 35, 20, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 35, 22, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 38, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 39, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 40, 19, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 40, 32, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 41, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[24, 41, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 0, 17, 1] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 1, 17, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 1, 37, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 2, 25, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 3, 7, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 3, 31, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 5, 8, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 5, 27, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 6, 18, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 8, 41, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 9, 11, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 9, 28, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 11, 24, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 11, 34, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 12, 10, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 14, 22, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 14, 30, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 15, 4, 1] 4\n", - "[50, 30, 8, 2] 0\n", - "[75, 45, 12, 3] 0\n", - "[100, 60, 16, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 18, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 19, 20, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 19, 22, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 20, 5, 1] 4\n", - "[50, 40, 10, 2] 4\n", - "[75, 60, 15, 3] 4\n", - "[100, 80, 20, 4] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 21, 27, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 22, 5, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 22, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 23, 30, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 25, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 25, 1, 1] -8\n", - "[50, 50, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 26, 36, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 27, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 28, 34, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 29, 36, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 30, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 30, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 31, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 32, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 33, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 34, 38, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 36, 16, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 37, 9, 1] 8\n", - "[50, 74, 18, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 40, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[25, 41, 12, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 2, 18, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 3, 9, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 4, 2, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 6, 5, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 7, 11, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 7, 28, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 9, 22, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 9, 30, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 11, 21, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 11, 39, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 12, 7, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 13, 18, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 15, 31, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 16, 24, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 17, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 17, 32, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 18, 8, 1] 8\n", - "[52, 36, 16, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 18, 35, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 19, 10, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 25, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 26, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 26, 1, 1] -8\n", - "[52, 52, 2, 2] -8\n", - "[78, 78, 3, 3] 0\n", - "[104, 104, 4, 4] 0\n", - "[130, 130, 5, 5] -4\n", - "[156, 156, 6, 6] 0\n", - "[182, 182, 7, 7] 0\n", - "[208, 208, 8, 8] -8\n", - "[234, 234, 9, 9] 0\n", - "[260, 260, 10, 10] 4\n", - "[286, 286, 11, 11] -4\n", - "[312, 312, 12, 12] 4\n", - "[338, 338, 13, 13] 8\n", - "[364, 364, 14, 14] -4\n", - "[390, 390, 15, 15] 0\n", - "[416, 416, 16, 16] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 28, 5, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 28, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 29, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 30, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 31, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 31, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 32, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 32, 10, 1] 8\n", - "[52, 64, 20, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 33, 9, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 34, 27, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 35, 36, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 36, 17, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 37, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 37, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 38, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 39, 4, 1] 0\n", - "[52, 78, 8, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 40, 26, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 40, 29, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 41, 3, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[26, 41, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 2, 40, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 3, 32, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 3, 39, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 5, 25, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 7, 20, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 8, 0, 1] 83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 9, 4, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 9, 10, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 10, 6, 1] 8\n", - "[54, 20, 12, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 13, 41, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 14, 7, 1] 8\n", - "[54, 28, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 14, 31, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 15, 24, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 15, 34, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 16, 5, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 16, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 17, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 18, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 18, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 19, 31, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 20, 2, 1] -4\n", - "[54, 40, 4, 2] -4\n", - "[81, 60, 6, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 20, 13, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 21, 25, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 22, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 23, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 25, 35, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 26, 14, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 26, 23, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 27, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 27, 1, 1] -8\n", - "[54, 54, 2, 2] -8\n", - "[81, 81, 3, 3] 0\n", - "[108, 108, 4, 4] -4\n", - "[135, 135, 5, 5] -4\n", - "[162, 162, 6, 6] 4\n", - "[189, 189, 7, 7] -4\n", - "[216, 216, 8, 8] -8\n", - "[243, 243, 9, 9] 4\n", - "[270, 270, 10, 10] 4\n", - "[297, 297, 11, 11] 0\n", - "[324, 324, 12, 12] 4\n", - "[351, 351, 13, 13] 4\n", - "[378, 378, 14, 14] -4\n", - "[405, 405, 15, 15] 4\n", - "[432, 432, 16, 16] 8\n", - "[459, 459, 17, 17] 0\n", - "[486, 486, 18, 18] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 29, 14, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 29, 19, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 33, 19, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 33, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 34, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 35, 9, 0] -75\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 36, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 36, 30, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 37, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 38, 36, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 40, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[27, 41, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 1, 31, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 2, 36, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 4, 35, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 6, 0, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 7, 26, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 8, 32, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 8, 39, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 9, 25, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 10, 8, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 10, 35, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 11, 1, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 12, 5, 1] 8\n", - "[56, 24, 10, 2] 4\n", - "[84, 36, 15, 3] 0\n", - "[112, 48, 20, 4] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 13, 7, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 14, 34, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 15, 40, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 17, 2, 1] -4\n", - "[56, 34, 4, 2] -4\n", - "[84, 51, 6, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 17, 13, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 18, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 19, 18, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 20, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 22, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 23, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 23, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 24, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 25, 16, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 26, 15, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 27, 19, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 27, 32, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 28, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 28, 1, 1] -8\n", - "[56, 56, 2, 2] -8\n", - "[84, 84, 3, 3] 0\n", - "[112, 112, 4, 4] -4\n", - "[140, 140, 5, 5] -4\n", - "[168, 168, 6, 6] 4\n", - "[196, 196, 7, 7] -4\n", - "[224, 224, 8, 8] -4\n", - "[252, 252, 9, 9] 0\n", - "[280, 280, 10, 10] 0\n", - "[308, 308, 11, 11] 0\n", - "[336, 336, 12, 12] 8\n", - "[364, 364, 13, 13] -4\n", - "[392, 392, 14, 14] 0\n", - "[420, 420, 15, 15] 8\n", - "[448, 448, 16, 16] 0\n", - "[476, 476, 17, 17] 4\n", - "[504, 504, 18, 18] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 30, 38, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 31, 26, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 31, 29, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 32, 18, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 34, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 34, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 35, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 35, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 37, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 40, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 40, 30, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[28, 41, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 2, 34, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 3, 9, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 6, 5, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 6, 21, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 7, 11, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 9, 30, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 10, 16, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 11, 32, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 11, 39, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 12, 36, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 13, 18, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 15, 7, 1] 8\n", - "[58, 30, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 15, 31, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 17, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 17, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 18, 8, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 18, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 21, 4, 1] 0\n", - "[58, 42, 8, 2] 4\n", - "[87, 63, 12, 3] 0\n", - "[116, 84, 16, 4] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 22, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 23, 41, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 24, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 25, 38, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 26, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 28, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 28, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 29, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 29, 1, 1] -8\n", - "[58, 58, 2, 2] -8\n", - "[87, 87, 3, 3] 0\n", - "[116, 116, 4, 4] -8\n", - "[145, 145, 5, 5] 0\n", - "[174, 174, 6, 6] 0\n", - "[203, 203, 7, 7] -8\n", - "[232, 232, 8, 8] 0\n", - "[261, 261, 9, 9] 4\n", - "[290, 290, 10, 10] -4\n", - "[319, 319, 11, 11] 4\n", - "[348, 348, 12, 12] 4\n", - "[377, 377, 13, 13] -4\n", - "[406, 406, 14, 14] 4\n", - "[435, 435, 15, 15] 4\n", - "[464, 464, 16, 16] 4\n", - "[493, 493, 17, 17] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 30, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 31, 11, 1] 8\n", - "[58, 62, 22, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 31, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 32, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 33, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 36, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 36, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 37, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 37, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 38, 40, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 39, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 39, 10, 1] 8\n", - "[58, 78, 20, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 40, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 41, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[29, 41, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 2, 10, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 3, 40, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 4, 14, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 4, 19, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 5, 11, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 6, 7, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 7, 35, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 8, 24, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 8, 34, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 9, 26, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 9, 29, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 10, 14, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 10, 23, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 11, 36, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 12, 18, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 13, 4, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 13, 10, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 14, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 16, 41, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 20, 9, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 21, 17, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 22, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 23, 25, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 24, 3, 1] -4\n", - "[60, 48, 6, 2] 0\n", - "[90, 72, 9, 3] 4\n", - "[120, 96, 12, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 26, 5, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 26, 21, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 27, 24, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 28, 36, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 29, 5, 1] 0\n", - "[60, 58, 10, 2] 4\n", - "[90, 87, 15, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 30, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 30, 1, 1] -8\n", - "[60, 60, 2, 2] -8\n", - "[90, 90, 3, 3] 0\n", - "[120, 120, 4, 4] -8\n", - "[150, 150, 5, 5] 0\n", - "[180, 180, 6, 6] 0\n", - "[210, 210, 7, 7] -8\n", - "[240, 240, 8, 8] 0\n", - "[270, 270, 9, 9] 0\n", - "[300, 300, 10, 10] -4\n", - "[330, 330, 11, 11] 8\n", - "[360, 360, 12, 12] 0\n", - "[390, 390, 13, 13] 0\n", - "[420, 420, 14, 14] 8\n", - "[450, 450, 15, 15] 0\n", - "[480, 480, 16, 16] 4\n", - "[510, 510, 17, 17] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 31, 12, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 32, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 33, 40, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 34, 16, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 35, 34, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 36, 8, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 36, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 39, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 39, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 40, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[30, 40, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 0, 6, 1] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 1, 6, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 1, 28, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 2, 17, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 3, 25, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 4, 36, 0] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 5, 12, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 7, 1, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 8, 4, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 8, 10, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 9, 38, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 13, 11, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 14, 27, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 15, 26, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 15, 29, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 17, 18, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 18, 32, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 18, 39, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 19, 8, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 19, 27, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 20, 41, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 21, 12, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 22, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 24, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 24, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 26, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 27, 10, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 30, 40, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 31, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 31, 1, 1] -8\n", - "[62, 62, 2, 2] -4\n", - "[93, 93, 3, 3] -4\n", - "[124, 124, 4, 4] -8\n", - "[155, 155, 5, 5] 0\n", - "[186, 186, 6, 6] 0\n", - "[217, 217, 7, 7] -8\n", - "[248, 248, 8, 8] 4\n", - "[279, 279, 9, 9] -4\n", - "[310, 310, 10, 10] 0\n", - "[341, 341, 11, 11] 4\n", - "[372, 372, 12, 12] -4\n", - "[403, 403, 13, 13] 8\n", - "[434, 434, 14, 14] 4\n", - "[465, 465, 15, 15] -4\n", - "[496, 496, 16, 16] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 32, 8, 1] 4\n", - "[62, 64, 16, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 32, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 34, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 34, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 35, 4, 1] 0\n", - "[62, 70, 8, 2] 12\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 36, 2, 1] -4\n", - "[62, 72, 4, 2] 4\n", - "[93, 108, 6, 3] -8\n", - "[124, 144, 8, 4] 0\n", - "[155, 180, 10, 5] 8\n", - "[186, 216, 12, 6] 4\n", - "[217, 252, 14, 7] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 36, 13, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 37, 34, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 38, 20, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 38, 22, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 39, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[31, 40, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 2, 15, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 3, 8, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 3, 27, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 5, 9, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 6, 3, 1] 8\n", - "[64, 12, 6, 2] 8\n", - "[96, 18, 9, 3] 0\n", - "[128, 24, 12, 4] 4\n", - "[160, 30, 15, 5] 4\n", - "[192, 36, 18, 6] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 7, 41, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 8, 6, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 8, 28, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 11, 29, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 11, 33, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 12, 38, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 13, 15, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 14, 13, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 15, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 16, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 17, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 18, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 19, 1, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 20, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 20, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 21, 9, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 22, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 23, 2, 1] -8\n", - "[64, 46, 4, 2] -4\n", - "[96, 69, 6, 3] 0\n", - "[128, 92, 8, 4] 8\n", - "[160, 115, 10, 5] -4\n", - "[192, 138, 12, 6] 8\n", - "[224, 161, 14, 7] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 23, 13, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 24, 36, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 25, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 25, 10, 1] 4\n", - "[64, 50, 20, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 26, 20, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 27, 11, 1] 8\n", - "[64, 54, 22, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 27, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 28, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 28, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 31, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 32, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 32, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 33, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 34, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 35, 6, 1] 0\n", - "[64, 70, 12, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 36, 40, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 39, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 40, 24, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[32, 41, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 1, 18, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 2, 24, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 2, 34, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 3, 0, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 4, 16, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 5, 4, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 6, 21, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 6, 39, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 7, 17, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 10, 16, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 11, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 11, 32, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 12, 36, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 13, 34, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 14, 41, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 15, 7, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 16, 9, 1] 8\n", - "[66, 32, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 17, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 17, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 18, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 20, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 21, 4, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 21, 10, 1] 8\n", - "[66, 42, 20, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 22, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 23, 41, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 24, 20, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 24, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 26, 13, 1] 8\n", - "[66, 52, 26, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 28, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 28, 39, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 29, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 30, 12, 1] 8\n", - "[66, 60, 24, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 31, 11, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 33, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 33, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 34, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 36, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 37, 23, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 38, 40, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 39, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 41, 26, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[33, 41, 29, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 0, 16, 1] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 1, 16, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 2, 29, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 2, 33, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 3, 4, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 4, 40, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 5, 23, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 8, 30, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 9, 2, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 10, 40, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 11, 25, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 12, 20, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 13, 3, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 13, 33, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 14, 6, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 14, 28, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 15, 27, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 18, 9, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 19, 6, 1] 4\n", - "[68, 38, 12, 2] 8\n", - "[102, 57, 18, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 20, 18, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 21, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 22, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 23, 11, 1] 8\n", - "[68, 46, 22, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 23, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 24, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 25, 36, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 28, 25, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 29, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 30, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 33, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 33, 10, 1] 4\n", - "[68, 66, 20, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 34, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 34, 1, 1] -8\n", - "[68, 68, 2, 2] -4\n", - "[102, 102, 3, 3] -4\n", - "[136, 136, 4, 4] -4\n", - "[170, 170, 5, 5] 4\n", - "[204, 204, 6, 6] -8\n", - "[238, 238, 7, 7] 0\n", - "[272, 272, 8, 8] -4\n", - "[306, 306, 9, 9] -4\n", - "[340, 340, 10, 10] 4\n", - "[374, 374, 11, 11] -4\n", - "[408, 408, 12, 12] 8\n", - "[442, 442, 13, 13] 0\n", - "[476, 476, 14, 14] 0\n", - "[510, 510, 15, 15] 8\n", - "[544, 544, 16, 16] 0\n", - "[578, 578, 17, 17] 8\n", - "[612, 612, 18, 18] 4\n", - "[646, 646, 19, 19] 4\n", - "[680, 680, 20, 20] 8\n", - "[714, 714, 21, 21] 0\n", - "[748, 748, 22, 22] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 35, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 35, 30, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 37, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 38, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 39, 38, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 40, 14, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 40, 19, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 41, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[34, 41, 39, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 0, 41, 1] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 1, 41, 0] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 2, 5, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 3, 14, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 3, 19, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 4, 6, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 4, 28, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 7, 22, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 7, 30, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 8, 1, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 10, 11, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 10, 28, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 11, 15, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 12, 9, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 13, 40, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 14, 36, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 16, 32, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 16, 39, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 17, 12, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 18, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 19, 7, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 22, 16, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 23, 36, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 24, 4, 1] -4\n", - "[70, 48, 8, 2] 0\n", - "[105, 72, 12, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 25, 8, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 25, 27, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 26, 38, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 27, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 29, 23, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 30, 16, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 31, 20, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 31, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 32, 7, 1] 0\n", - "[70, 64, 14, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 32, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 33, 14, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 33, 23, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 35, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 35, 1, 1] -8\n", - "[70, 70, 2, 2] -4\n", - "[105, 105, 3, 3] -8\n", - "[140, 140, 4, 4] -4\n", - "[175, 175, 5, 5] 0\n", - "[210, 210, 6, 6] -8\n", - "[245, 245, 7, 7] 4\n", - "[280, 280, 8, 8] -4\n", - "[315, 315, 9, 9] 0\n", - "[350, 350, 10, 10] 0\n", - "[385, 385, 11, 11] 0\n", - "[420, 420, 12, 12] 8\n", - "[455, 455, 13, 13] -4\n", - "[490, 490, 14, 14] 4\n", - "[525, 525, 15, 15] 0\n", - "[560, 560, 16, 16] 8\n", - "[595, 595, 17, 17] 8\n", - "[630, 630, 18, 18] 4\n", - "[665, 665, 19, 19] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 37, 12, 0] -71\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 39, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 40, 25, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[35, 41, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 0, 38, 1] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 1, 38, 0] -31\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 2, 6, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 2, 28, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 3, 37, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 4, 7, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 4, 31, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 6, 20, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 6, 22, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 7, 9, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 9, 14, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 9, 23, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 10, 7, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 11, 30, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 12, 29, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 12, 33, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 13, 6, 1] 8\n", - "[72, 26, 12, 2] 4\n", - "[108, 39, 18, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 14, 35, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 15, 3, 1] 0\n", - "[72, 30, 6, 2] -4\n", - "[108, 45, 9, 3] 4\n", - "[144, 60, 12, 4] 8\n", - "[180, 75, 15, 5] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 16, 17, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 18, 5, 1] 0\n", - "[72, 36, 10, 2] 4\n", - "[108, 54, 15, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 19, 12, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 20, 10, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 21, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 23, 8, 1] 4\n", - "[72, 46, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 23, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 24, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 24, 39, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 25, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 26, 25, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 28, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 28, 30, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 29, 25, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 31, 9, 1] 4\n", - "[72, 62, 18, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 32, 12, 1] 8\n", - "[72, 64, 24, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 34, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 34, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 35, 26, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 36, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 36, 1, 1] -8\n", - "[72, 72, 2, 2] -4\n", - "[108, 108, 3, 3] -8\n", - "[144, 144, 4, 4] -4\n", - "[180, 180, 5, 5] 0\n", - "[216, 216, 6, 6] -8\n", - "[252, 252, 7, 7] 0\n", - "[288, 288, 8, 8] -8\n", - "[324, 324, 9, 9] 0\n", - "[360, 360, 10, 10] 0\n", - "[396, 396, 11, 11] 4\n", - "[432, 432, 12, 12] 4\n", - "[468, 468, 13, 13] 0\n", - "[504, 504, 14, 14] 8\n", - "[540, 540, 15, 15] -4\n", - "[576, 576, 16, 16] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 38, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[36, 39, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 1, 25, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 3, 36, 0] -39\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 4, 15, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 5, 20, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 6, 24, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 7, 3, 1] 4\n", - "[74, 14, 6, 2] 0\n", - "[111, 21, 9, 3] 4\n", - "[148, 28, 12, 4] 8\n", - "[185, 35, 15, 5] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 8, 40, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 9, 17, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 9, 37, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 10, 15, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 11, 9, 1] 8\n", - "[74, 22, 18, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 12, 41, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 16, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 17, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 20, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 20, 39, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 21, 20, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 21, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 22, 19, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 22, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 24, 11, 1] 4\n", - "[74, 48, 22, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 24, 28, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 25, 2, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 25, 13, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 27, 5, 1] -4\n", - "[74, 54, 10, 2] 0\n", - "[111, 81, 15, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 30, 14, 1] 8\n", - "[74, 60, 28, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 30, 19, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 31, 16, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 32, 30, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 34, 6, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 34, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 35, 40, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 36, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 36, 33, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 37, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 37, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 38, 18, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 39, 22, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 39, 30, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 40, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 41, 8, 1] 0\n", - "[74, 82, 16, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[37, 41, 35, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 0, 36, 1] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 1, 36, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 3, 15, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 5, 18, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 6, 2, 1] 4\n", - "[76, 12, 4, 2] 0\n", - "[114, 18, 6, 3] 0\n", - "[152, 24, 8, 4] 0\n", - "[190, 30, 10, 5] 4\n", - "[228, 36, 12, 6] 8\n", - "[266, 42, 14, 7] 8\n", - "[304, 48, 16, 8] 8\n", - "[342, 54, 18, 9] 4\n", - "[380, 60, 20, 10] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 6, 13, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 7, 4, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 7, 10, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 8, 23, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 9, 7, 1] 8\n", - "[76, 18, 14, 2] 8\n", - "[114, 27, 21, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 9, 31, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 10, 20, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 12, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 12, 32, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 14, 9, 1] 8\n", - "[76, 28, 18, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 15, 21, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 15, 39, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 17, 16, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 20, 6, 1] 0\n", - "[76, 40, 12, 2] 4\n", - "[114, 60, 18, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 21, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 22, 6, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 22, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 23, 9, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 25, 26, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 25, 29, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 26, 35, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 27, 38, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 28, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 29, 12, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 30, 11, 1] 4\n", - "[76, 60, 22, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 30, 28, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 31, 4, 1] -8\n", - "[76, 62, 8, 2] 0\n", - "[114, 93, 12, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 32, 24, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 33, 12, 1] 4\n", - "[76, 66, 24, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 34, 25, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 35, 14, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 35, 23, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 37, 3, 1] -8\n", - "[76, 74, 6, 2] 4\n", - "[114, 111, 9, 3] 4\n", - "[152, 148, 12, 4] 8\n", - "[190, 185, 15, 5] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 38, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 38, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 39, 24, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[38, 39, 34, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 2, 12, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 3, 27, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 5, 9, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 6, 3, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 6, 33, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 7, 40, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 8, 11, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 8, 28, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 11, 26, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 11, 29, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 13, 15, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 14, 2, 1] -4\n", - "[78, 28, 4, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 14, 13, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 15, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 16, 8, 1] 4\n", - "[78, 32, 16, 2] 4\n", - "[117, 48, 24, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 16, 35, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 18, 7, 1] 0\n", - "[78, 36, 14, 2] 4\n", - "[117, 54, 21, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 18, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 19, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 20, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 21, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 23, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 24, 36, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 25, 10, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 26, 20, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 26, 22, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 27, 11, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 28, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 28, 33, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 29, 20, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 30, 25, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 31, 41, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 32, 1, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 34, 36, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 35, 6, 0] -83\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 35, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 36, 5, 1] -4\n", - "[78, 72, 10, 2] 4\n", - "[117, 108, 15, 3] 8\n", - "[156, 144, 20, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 38, 16, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 39, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 39, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 41, 24, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[39, 41, 34, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 0, 12, 1] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 1, 12, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 2, 8, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 2, 27, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 3, 22, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 3, 30, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 4, 34, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 5, 13, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 7, 21, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 7, 39, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 8, 37, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 9, 15, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 10, 24, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 10, 34, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 11, 4, 1] 0\n", - "[80, 22, 8, 2] -8\n", - "[120, 33, 12, 3] 0\n", - "[160, 44, 16, 4] 8\n", - "[200, 55, 20, 5] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 12, 11, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 13, 8, 1] 8\n", - "[80, 26, 16, 2] 0\n", - "[120, 39, 24, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 13, 35, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 14, 16, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 15, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 15, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 16, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 17, 10, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 19, 16, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 21, 2, 1] -8\n", - "[80, 42, 4, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 21, 13, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 23, 3, 1] -8\n", - "[80, 46, 6, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 25, 41, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 30, 31, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 31, 5, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 31, 21, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 33, 30, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 35, 17, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 35, 37, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 36, 19, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 36, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 38, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 38, 33, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 39, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 40, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 40, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[40, 41, 9, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 0, 35, 1] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 1, 8, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 1, 35, 0] -35\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 4, 24, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 5, 2, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 6, 4, 1] 8\n", - "[82, 12, 8, 2] 0\n", - "[123, 18, 12, 3] 4\n", - "[164, 24, 16, 4] 4\n", - "[205, 30, 20, 5] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 7, 19, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 7, 32, 0] -43\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 8, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 9, 12, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 11, 10, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 12, 17, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 12, 37, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 13, 27, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 14, 3, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 14, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 15, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 16, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 16, 30, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 19, 3, 1] -4\n", - "[82, 38, 6, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 20, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 22, 7, 1] 0\n", - "[82, 44, 14, 2] 0\n", - "[123, 66, 21, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 22, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 23, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 23, 33, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 25, 40, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 26, 18, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 27, 25, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 28, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 28, 10, 1] 4\n", - "[82, 56, 20, 2] 8\n", - "[123, 84, 30, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 30, 7, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 31, 32, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 31, 39, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 32, 16, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 36, 14, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 36, 23, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 37, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 38, 26, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 39, 16, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 40, 13, 1] 8\n", - "[82, 80, 26, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 41, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83)\n", - "[ characters ] sigma value\n", - "[41, 41, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 0, 1, 1] 0\n", - "[0, 0, 2, 2] 0\n", - "[0, 0, 3, 3] 0\n", - "[0, 0, 4, 4] 0\n", - "[0, 0, 5, 5] 0\n", - "[0, 0, 6, 6] 0\n", - "[0, 0, 7, 7] 0\n", - "[0, 0, 8, 8] 0\n", - "[0, 0, 9, 9] 0\n", - "[0, 0, 10, 10] 4\n", - "[0, 0, 11, 11] 4\n", - "[0, 0, 12, 12] 0\n", - "[0, 0, 13, 13] 0\n", - "[0, 0, 14, 14] 0\n", - "[0, 0, 15, 15] 0\n", - "[0, 0, 16, 16] 4\n", - "[0, 0, 17, 17] 4\n", - "[0, 0, 18, 18] 4\n", - "[0, 0, 19, 19] 4\n", - "[0, 0, 20, 20] 0\n", - "[0, 0, 21, 21] 0\n", - "[0, 0, 22, 22] 4\n", - "[0, 0, 23, 23] 4\n", - "[0, 0, 24, 24] 4\n", - "[0, 0, 25, 25] 4\n", - "[0, 0, 26, 26] 4\n", - "[0, 0, 27, 27] 4\n", - "[0, 0, 28, 28] 4\n", - "[0, 0, 29, 29] 4\n", - "[0, 0, 30, 30] 4\n", - "[0, 0, 31, 31] 4\n", - "[0, 0, 32, 32] 4\n", - "[0, 0, 33, 33] 4\n", - "[0, 0, 34, 34] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 1, 1, 0] 0\n", - "[0, 2, 2, 0] 0\n", - "[0, 3, 3, 0] 0\n", - "[0, 4, 4, 0] -4\n", - "[0, 5, 5, 0] -4\n", - "[0, 6, 6, 0] -4\n", - "[0, 7, 7, 0] -4\n", - "[0, 8, 8, 0] -4\n", - "[0, 9, 9, 0] -4\n", - "[0, 10, 10, 0] -4\n", - "[0, 11, 11, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 1, 38, 1] 127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 2, 2, 0] 0\n", - "[0, 4, 4, 0] -4\n", - "[0, 6, 6, 0] -4\n", - "[0, 8, 8, 0] -4\n", - "[0, 10, 10, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 3, 3, 0] 0\n", - "[0, 6, 6, 0] -4\n", - "[0, 9, 9, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 4, 4, 0] -4\n", - "[0, 8, 8, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 4, 29, 1] 119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 5, 5, 0] -4\n", - "[0, 10, 10, 0] -4\n", - "[0, 15, 15, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 5, 51, 1] 119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 6, 6, 0] -4\n", - "[0, 12, 12, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 7, 7, 0] -4\n", - "[0, 14, 14, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 7, 16, 1] 107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 8, 8, 0] -4\n", - "[0, 16, 16, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 9, 9, 0] -4\n", - "[0, 18, 18, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 9, 44, 1] 111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 10, 10, 0] -4\n", - "[0, 20, 20, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 11, 11, 0] -4\n", - "[0, 22, 22, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 11, 15, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 12, 12, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 13, 13, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 14, 14, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 15, 15, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 16, 16, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 17, 17, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 18, 4, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 18, 18, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 19, 19, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 20, 20, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 20, 35, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 21, 21, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 21, 37, 1] 95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 22, 22, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 23, 18, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 23, 23, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 24, 24, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 25, 25, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 25, 27, 1] 91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 26, 26, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 26, 33, 1] 91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 27, 3, 1] 67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 27, 27, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 28, 8, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 28, 28, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 29, 11, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 29, 29, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 30, 30, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 31, 31, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 32, 32, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 32, 43, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 33, 33, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 33, 36, 1] 83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 34, 34, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 35, 14, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 35, 35, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 36, 24, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 36, 36, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 37, 37, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 38, 38, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 39, 39, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 40, 40, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 40, 46, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 41, 31, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 41, 41, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 42, 23, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 42, 42, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 43, 43, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 44, 17, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 44, 44, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 45, 45, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 46, 46, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 47, 47, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 48, 48, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 49, 41, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 49, 49, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 50, 21, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 50, 50, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[0, 51, 51, 0] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 0, 0, 1] 0\n", - "[2, 0, 0, 2] 0\n", - "[3, 0, 0, 3] 0\n", - "[4, 0, 0, 4] 4\n", - "[5, 0, 0, 5] 0\n", - "[6, 0, 0, 6] 0\n", - "[7, 0, 0, 7] 0\n", - "[8, 0, 0, 8] 0\n", - "[9, 0, 0, 9] 0\n", - "[10, 0, 0, 10] 4\n", - "[11, 0, 0, 11] 4\n", - "[12, 0, 0, 12] 4\n", - "[13, 0, 0, 13] 4\n", - "[14, 0, 0, 14] 4\n", - "[15, 0, 0, 15] 0\n", - "[16, 0, 0, 16] 4\n", - "[17, 0, 0, 17] 4\n", - "[18, 0, 0, 18] 4\n", - "[19, 0, 0, 19] 4\n", - "[20, 0, 0, 20] 4\n", - "[21, 0, 0, 21] 4\n", - "[22, 0, 0, 22] 8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 1, 0, 0] 0\n", - "[2, 2, 0, 0] 0\n", - "[3, 3, 0, 0] 0\n", - "[4, 4, 0, 0] 0\n", - "[5, 5, 0, 0] -4\n", - "[6, 6, 0, 0] -4\n", - "[7, 7, 0, 0] -4\n", - "[8, 8, 0, 0] -4\n", - "[9, 9, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[11, 11, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[13, 13, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[15, 15, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 1, 1, 1] 0\n", - "[2, 2, 2, 2] 0\n", - "[3, 3, 3, 3] 0\n", - "[4, 4, 4, 4] 0\n", - "[5, 5, 5, 5] -4\n", - "[6, 6, 6, 6] -4\n", - "[7, 7, 7, 7] -4\n", - "[8, 8, 8, 8] -4\n", - "[9, 9, 9, 9] -4\n", - "[10, 10, 10, 10] 0\n", - "[11, 11, 11, 11] 0\n", - "[12, 12, 12, 12] -4\n", - "[13, 13, 13, 13] -4\n", - "[14, 14, 14, 14] -4\n", - "[15, 15, 15, 15] -8\n", - "[16, 16, 16, 16] -4\n", - "[17, 17, 17, 17] -4\n", - "[18, 18, 18, 18] -4\n", - "[19, 19, 19, 19] -4\n", - "[20, 20, 20, 20] -8\n", - "[21, 21, 21, 21] -8\n", - "[22, 22, 22, 22] -4\n", - "[23, 23, 23, 23] -4\n", - "[24, 24, 24, 24] -8\n", - "[25, 25, 25, 25] -8\n", - "[26, 26, 26, 26] -8\n", - "[27, 27, 27, 27] -8\n", - "[28, 28, 28, 28] -8\n", - "[29, 29, 29, 29] -8\n", - "[30, 30, 30, 30] -8\n", - "[31, 31, 31, 31] -8\n", - "[32, 32, 32, 32] -8\n", - "[33, 33, 33, 33] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 2, 2, 1] 0\n", - "[2, 4, 4, 2] -4\n", - "[3, 6, 6, 3] -4\n", - "[4, 8, 8, 4] 0\n", - "[5, 10, 10, 5] -4\n", - "[6, 12, 12, 6] -8\n", - "[7, 14, 14, 7] -8\n", - "[8, 16, 16, 8] -8\n", - "[9, 18, 18, 9] -8\n", - "[10, 20, 20, 10] -8\n", - "[11, 22, 22, 11] -8\n", - "[12, 24, 24, 12] -8\n", - "[13, 26, 26, 13] -8\n", - "[14, 28, 28, 14] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 3, 3, 1] 0\n", - "[2, 6, 6, 2] -4\n", - "[3, 9, 9, 3] -4\n", - "[4, 12, 12, 4] -4\n", - "[5, 15, 15, 5] -8\n", - "[6, 18, 18, 6] -8\n", - "[7, 21, 21, 7] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 3, 27, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 4, 4, 1] -4\n", - "[2, 8, 8, 2] -4\n", - "[3, 12, 12, 3] -8\n", - "[4, 16, 16, 4] -4\n", - "[5, 20, 20, 5] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 4, 18, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 5, 5, 1] -4\n", - "[2, 10, 10, 2] -4\n", - "[3, 15, 15, 3] -8\n", - "[4, 20, 20, 4] -8\n", - "[5, 25, 25, 5] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 6, 6, 1] -4\n", - "[2, 12, 12, 2] -8\n", - "[3, 18, 18, 3] -8\n", - "[4, 24, 24, 4] -8\n", - "[5, 30, 30, 5] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 7, 7, 1] -4\n", - "[2, 14, 14, 2] -8\n", - "[3, 21, 21, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 8, 8, 1] -4\n", - "[2, 16, 16, 2] -8\n", - "[3, 24, 24, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 8, 28, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 9, 9, 1] -4\n", - "[2, 18, 18, 2] -8\n", - "[3, 27, 27, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 10, 10, 1] -4\n", - "[2, 20, 20, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 11, 11, 1] -4\n", - "[2, 22, 22, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 11, 29, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 12, 12, 1] -8\n", - "[2, 24, 24, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 13, 13, 1] -8\n", - "[2, 26, 26, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 14, 14, 1] -8\n", - "[2, 28, 28, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 14, 35, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 15, 11, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 15, 15, 1] -8\n", - "[2, 30, 30, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 16, 7, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 16, 16, 1] -8\n", - "[2, 32, 32, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 17, 17, 1] -8\n", - "[2, 34, 34, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 17, 44, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 18, 18, 1] -8\n", - "[2, 36, 36, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 18, 23, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 19, 19, 1] -8\n", - "[2, 38, 38, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 20, 20, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 21, 21, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 21, 50, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 22, 22, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 23, 23, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 23, 42, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 24, 24, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 24, 36, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 25, 25, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 26, 26, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 27, 25, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 27, 27, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 28, 28, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 29, 4, 0] -139\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 29, 29, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 30, 30, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 31, 31, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 31, 41, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 32, 32, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 33, 26, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 33, 33, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 34, 34, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 35, 20, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 35, 35, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 36, 33, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 36, 36, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 37, 21, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 37, 37, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 38, 1, 0] -147\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 38, 38, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 39, 39, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 40, 40, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 41, 41, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 41, 49, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 42, 42, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 43, 32, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 43, 43, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 44, 9, 0] -139\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 44, 44, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 45, 45, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 46, 40, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 46, 46, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 47, 47, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 48, 48, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 49, 49, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 50, 50, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 51, 5, 0] -147\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[1, 51, 51, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 0, 10, 1] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 1, 10, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 2, 0, 0] 0\n", - "[4, 4, 0, 0] 0\n", - "[6, 6, 0, 0] -4\n", - "[8, 8, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[16, 16, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 2, 1, 1] 0\n", - "[4, 4, 2, 2] 0\n", - "[6, 6, 3, 3] -4\n", - "[8, 8, 4, 4] -4\n", - "[10, 10, 5, 5] -4\n", - "[12, 12, 6, 6] -4\n", - "[14, 14, 7, 7] -4\n", - "[16, 16, 8, 8] -8\n", - "[18, 18, 9, 9] -8\n", - "[20, 20, 10, 10] -4\n", - "[22, 22, 11, 11] -4\n", - "[24, 24, 12, 12] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 4, 42, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 6, 41, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 6, 49, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 7, 47, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 8, 24, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 8, 36, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 10, 32, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 11, 18, 1] 4\n", - "[4, 22, 36, 2] -4\n", - "[6, 33, 54, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 11, 23, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 12, 48, 1] 8\n", - "[4, 24, 96, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 13, 28, 1] 4\n", - "[4, 26, 56, 2] -8\n", - "[6, 39, 84, 3] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 15, 4, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 15, 18, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 16, 47, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 17, 39, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 19, 7, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 21, 5, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 21, 51, 1] -4\n", - "[4, 42, 102, 2] -44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 22, 45, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 24, 26, 1] -8\n", - "[4, 48, 52, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 25, 2, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 26, 40, 1] -8\n", - "[4, 52, 80, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 27, 2, 0] -135\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 28, 33, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 28, 36, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 29, 23, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 29, 42, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 30, 22, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 31, 37, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 32, 14, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 33, 40, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 33, 46, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 34, 15, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 36, 46, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 37, 51, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 39, 30, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 40, 19, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 41, 21, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 41, 37, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 42, 3, 0] -143\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 44, 39, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 45, 8, 0] -139\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 46, 19, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 48, 31, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 49, 21, 1] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 49, 50, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 50, 5, 1] -44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[2, 51, 34, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 2, 43, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 3, 0, 0] 0\n", - "[6, 6, 0, 0] -4\n", - "[9, 9, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[15, 15, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 3, 1, 1] 0\n", - "[6, 6, 2, 2] -4\n", - "[9, 9, 3, 3] -4\n", - "[12, 12, 4, 4] -4\n", - "[15, 15, 5, 5] -8\n", - "[18, 18, 6, 6] -8\n", - "[21, 21, 7, 7] -8\n", - "[24, 24, 8, 8] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 4, 25, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 4, 27, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 5, 4, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 5, 29, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 6, 50, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 7, 12, 1] 4\n", - "[6, 14, 24, 2] 4\n", - "[9, 21, 36, 3] 0\n", - "[12, 28, 48, 4] 0\n", - "[15, 35, 60, 5] -4\n", - "[18, 42, 72, 6] -8\n", - "[21, 49, 84, 7] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 8, 40, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 8, 46, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 9, 22, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 10, 20, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 10, 35, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 11, 3, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 12, 41, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[3, 12, 49, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 13, 26, 1] 8\n", - "[6, 26, 52, 2] -8\n", - "[9, 39, 78, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 16, 12, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 18, 25, 1] 0\n", - "[6, 36, 50, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 20, 17, 1] -8\n", - "[6, 40, 34, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 20, 44, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 22, 8, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 22, 28, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 24, 19, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 26, 7, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 26, 16, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 27, 0, 1] 67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 28, 40, 1] -8\n", - "[6, 56, 80, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 29, 3, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 29, 27, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 30, 45, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 31, 5, 0] -135\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 31, 51, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 33, 16, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 34, 18, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 34, 23, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 35, 17, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 36, 19, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 38, 32, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 40, 47, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 41, 5, 1] -40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 42, 2, 0] -143\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 45, 33, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 45, 36, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 47, 48, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 48, 21, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 48, 37, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 49, 34, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 50, 15, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 51, 11, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[3, 51, 29, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 2, 20, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 2, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 3, 32, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 4, 0, 0] 0\n", - "[8, 8, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[16, 16, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 4, 1, 1] 0\n", - "[8, 8, 2, 2] -4\n", - "[12, 12, 3, 3] -4\n", - "[16, 16, 4, 4] -8\n", - "[20, 20, 5, 5] -8\n", - "[24, 24, 6, 6] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 5, 3, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 7, 31, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 7, 41, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 8, 7, 1] 0\n", - "[8, 16, 14, 2] -4\n", - "[12, 24, 21, 3] -4\n", - "[16, 32, 28, 4] -4\n", - "[20, 40, 35, 5] 0\n", - "[24, 48, 42, 6] -4\n", - "[28, 56, 49, 7] -4\n", - "[32, 64, 56, 8] 0\n", - "[36, 72, 63, 9] 4\n", - "[40, 80, 70, 10] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 9, 13, 1] 4\n", - "[8, 18, 26, 2] 4\n", - "[12, 27, 39, 3] 0\n", - "[16, 36, 52, 4] -4\n", - "[20, 45, 65, 5] -4\n", - "[24, 54, 78, 6] -8\n", - "[28, 63, 91, 7] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 11, 38, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 12, 5, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 12, 51, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 13, 16, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 15, 2, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 16, 31, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 17, 45, 1] 4\n", - "[8, 34, 90, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 18, 0, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 19, 6, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 20, 30, 1] 0\n", - "[8, 40, 60, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 21, 23, 1] -4\n", - "[8, 42, 46, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 21, 42, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 22, 46, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 24, 47, 1] -4\n", - "[8, 48, 94, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 29, 1, 0] -135\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 29, 38, 1] -8\n", - "[8, 58, 76, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 30, 24, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 30, 36, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 31, 11, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 31, 15, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 32, 9, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 32, 44, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 34, 25, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 34, 27, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 35, 30, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 37, 18, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 37, 23, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 39, 8, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 39, 28, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 41, 11, 1] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 41, 29, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 42, 10, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 43, 17, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 43, 44, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 44, 13, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 45, 19, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 46, 12, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 47, 37, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 48, 34, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 49, 4, 0] -143\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 49, 29, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[4, 50, 42, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 0, 39, 1] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 1, 39, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 2, 17, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 2, 44, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 5, 0, 0] -4\n", - "[10, 10, 0, 0] -4\n", - "[15, 15, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 5, 1, 1] -4\n", - "[10, 10, 2, 2] -4\n", - "[15, 15, 3, 3] -8\n", - "[20, 20, 4, 4] -8\n", - "[25, 25, 5, 5] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 7, 5, 1] -4\n", - "[10, 14, 10, 2] 0\n", - "[15, 21, 15, 3] -4\n", - "[20, 28, 20, 4] 0\n", - "[25, 35, 25, 5] 0\n", - "[30, 42, 30, 6] 0\n", - "[35, 49, 35, 7] 0\n", - "[40, 56, 40, 8] 0\n", - "[45, 63, 45, 9] -4\n", - "[50, 70, 50, 10] 4\n", - "[55, 77, 55, 11] 8\n", - "[60, 84, 60, 12] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 9, 46, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 10, 30, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 11, 32, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 12, 4, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 12, 29, 1] 8\n", - "[10, 24, 58, 2] 0\n", - "[15, 36, 87, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 13, 12, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 14, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 15, 32, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 15, 43, 1] 8\n", - "[10, 30, 86, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 16, 5, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 16, 51, 1] 4\n", - "[10, 32, 102, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 17, 26, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 17, 33, 1] 4\n", - "[10, 34, 66, 2] -8\n", - "[15, 51, 99, 3] -36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 18, 14, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 19, 50, 1] 0\n", - "[10, 38, 100, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 20, 13, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 21, 2, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 23, 14, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 23, 35, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 24, 6, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 26, 31, 1] -8\n", - "[10, 52, 62, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 26, 41, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 28, 48, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 30, 19, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 31, 3, 0] -135\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 32, 22, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 33, 31, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 35, 45, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 36, 6, 1] -36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 38, 9, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 39, 40, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 40, 37, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 41, 3, 1] -40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 41, 27, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 42, 20, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 42, 35, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 44, 26, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 46, 49, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 48, 23, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 48, 42, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 49, 25, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 49, 27, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[5, 50, 2, 1] -44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 51, 1, 0] -147\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[5, 51, 38, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 0, 45, 1] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 1, 45, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 2, 22, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 3, 30, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 4, 17, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 5, 14, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 5, 35, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 6, 0, 0] -4\n", - "[12, 12, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 6, 1, 1] -4\n", - "[12, 12, 2, 2] -4\n", - "[18, 18, 3, 3] -8\n", - "[24, 24, 4, 4] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 7, 23, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 7, 42, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 8, 21, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 8, 50, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 9, 47, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 10, 8, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 13, 37, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 14, 26, 1] 8\n", - "[12, 28, 52, 2] 0\n", - "[18, 42, 78, 3] -8\n", - "[24, 56, 104, 4] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 16, 18, 1] 0\n", - "[12, 32, 36, 2] -4\n", - "[18, 48, 54, 3] -8\n", - "[24, 64, 72, 4] 0\n", - "[30, 80, 90, 5] 4\n", - "[36, 96, 108, 6] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 16, 23, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 18, 17, 1] -4\n", - "[12, 36, 34, 2] -4\n", - "[18, 54, 51, 3] -8\n", - "[24, 72, 68, 4] 8\n", - "[30, 90, 85, 5] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 18, 44, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 19, 4, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 19, 29, 1] 0\n", - "[12, 38, 58, 2] -8\n", - "[18, 57, 87, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 20, 40, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 20, 46, 1] 0\n", - "[12, 40, 92, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 21, 32, 1] 0\n", - "[12, 42, 64, 2] -8\n", - "[18, 63, 96, 3] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 22, 6, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 23, 9, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 23, 44, 1] -4\n", - "[12, 46, 88, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 24, 5, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 24, 51, 1] -4\n", - "[12, 48, 102, 2] -36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 26, 34, 1] -4\n", - "[12, 52, 68, 2] -8\n", - "[18, 78, 102, 3] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 27, 30, 1] -8\n", - "[12, 54, 60, 2] -8\n", - "[18, 81, 90, 3] -4\n", - "[24, 108, 120, 4] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 28, 50, 1] -8\n", - "[12, 56, 100, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 30, 12, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 32, 24, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 33, 34, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 34, 20, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 35, 46, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 36, 5, 1] -36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 37, 32, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 37, 43, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 40, 15, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 41, 10, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 42, 9, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 43, 28, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 44, 47, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 45, 41, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 45, 49, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 48, 38, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 49, 10, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[6, 51, 14, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 0, 40, 1] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 1, 40, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 1, 46, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 2, 26, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 2, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 3, 8, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 3, 28, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 5, 39, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 6, 20, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 7, 0, 0] -4\n", - "[14, 14, 0, 0] -4\n", - "[21, 21, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 7, 1, 1] -4\n", - "[14, 14, 2, 2] -4\n", - "[21, 21, 3, 3] -8\n", - "[28, 28, 4, 4] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 8, 4, 1] -4\n", - "[14, 16, 8, 2] 0\n", - "[21, 24, 12, 3] -4\n", - "[28, 32, 16, 4] 0\n", - "[35, 40, 20, 5] -4\n", - "[42, 48, 24, 6] 0\n", - "[49, 56, 28, 7] -4\n", - "[56, 64, 32, 8] 0\n", - "[63, 72, 36, 9] 4\n", - "[70, 80, 40, 10] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 8, 18, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 9, 41, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 9, 49, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 10, 19, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 11, 22, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 13, 11, 1] 0\n", - "[14, 26, 22, 2] 0\n", - "[21, 39, 33, 3] 0\n", - "[28, 52, 44, 4] 0\n", - "[35, 65, 55, 5] 4\n", - "[42, 78, 66, 6] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 13, 29, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 16, 1, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 16, 38, 1] 8\n", - "[14, 32, 76, 2] 0\n", - "[21, 48, 114, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 17, 31, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 19, 2, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 21, 17, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 22, 34, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 23, 45, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 24, 42, 1] 0\n", - "[14, 48, 84, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 25, 24, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 26, 3, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 27, 28, 1] -8\n", - "[14, 54, 56, 2] -8\n", - "[21, 81, 84, 3] 8\n", - "[28, 108, 112, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 28, 18, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 28, 23, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 29, 22, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 30, 50, 1] -8\n", - "[14, 60, 100, 2] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 32, 7, 1] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 38, 46, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 39, 37, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 40, 25, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 42, 45, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 43, 7, 0] -135\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 43, 16, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 44, 31, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 44, 41, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 45, 15, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 46, 25, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 46, 27, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 47, 10, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 48, 14, 1] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 48, 35, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 50, 17, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 50, 44, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[7, 51, 9, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 1, 12, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 3, 7, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 4, 40, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 4, 46, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 5, 8, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 6, 30, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 8, 0, 0] -4\n", - "[16, 16, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 8, 1, 1] -4\n", - "[16, 16, 2, 2] -8\n", - "[24, 24, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 9, 11, 1] 8\n", - "[16, 18, 22, 2] 8\n", - "[24, 27, 33, 3] 8\n", - "[32, 36, 44, 4] 8\n", - "[40, 45, 55, 5] 4\n", - "[48, 54, 66, 6] 0\n", - "[56, 63, 77, 7] 0\n", - "[64, 72, 88, 8] -4\n", - "[72, 81, 99, 9] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 9, 29, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 10, 6, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 11, 26, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 12, 9, 1] 0\n", - "[16, 24, 18, 2] 0\n", - "[24, 36, 27, 3] 0\n", - "[32, 48, 36, 4] 4\n", - "[40, 60, 45, 5] 4\n", - "[48, 72, 54, 6] 8\n", - "[56, 84, 63, 7] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 13, 38, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 14, 21, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 14, 37, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 15, 26, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 15, 33, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 17, 15, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 18, 40, 1] 8\n", - "[16, 36, 80, 2] -8\n", - "[24, 54, 120, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 19, 20, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 19, 35, 1] 8\n", - "[16, 38, 70, 2] -4\n", - "[24, 57, 105, 3] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 20, 50, 1] 4\n", - "[16, 40, 100, 2] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 21, 45, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 22, 3, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 22, 27, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 24, 10, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 25, 47, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 26, 32, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 26, 43, 1] 0\n", - "[16, 52, 86, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 28, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 29, 46, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 30, 42, 1] -4\n", - "[16, 60, 84, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 32, 31, 1] -8\n", - "[16, 64, 62, 2] -4\n", - "[24, 96, 93, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 32, 41, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 33, 43, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 34, 28, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 35, 21, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 35, 50, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 36, 10, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 38, 12, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 39, 4, 1] -36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 39, 18, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 41, 22, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 42, 19, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 43, 31, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 44, 11, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 44, 15, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 45, 2, 0] -139\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 49, 22, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 50, 45, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[8, 51, 13, 1] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 0, 34, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 1, 34, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 2, 51, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 3, 49, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 4, 48, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 6, 26, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 6, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 7, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 9, 0, 0] -4\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 9, 1, 1] -4\n", - "[18, 18, 2, 2] -8\n", - "[27, 27, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 10, 15, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 11, 12, 1] 4\n", - "[18, 22, 24, 2] 8\n", - "[27, 33, 36, 3] 4\n", - "[36, 44, 48, 4] 4\n", - "[45, 55, 60, 5] 4\n", - "[54, 66, 72, 6] 4\n", - "[63, 77, 84, 7] 8\n", - "[72, 88, 96, 8] 4\n", - "[81, 99, 108, 9] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 12, 8, 1] 0\n", - "[18, 24, 16, 2] 0\n", - "[27, 36, 24, 3] 0\n", - "[36, 48, 32, 4] 4\n", - "[45, 60, 40, 5] 4\n", - "[54, 72, 48, 6] 8\n", - "[63, 84, 56, 7] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 12, 28, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[9, 14, 42, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 15, 12, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 16, 22, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 17, 38, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 18, 48, 1] 8\n", - "[18, 36, 96, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 21, 19, 1] 0\n", - "[18, 42, 38, 2] -4\n", - "[27, 63, 57, 3] 0\n", - "[36, 84, 76, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 23, 6, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 24, 17, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 25, 21, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 25, 37, 1] 0\n", - "[18, 50, 74, 2] -8\n", - "[27, 75, 111, 3] -8\n", - "[36, 100, 148, 4] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 26, 9, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 27, 37, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 30, 43, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 31, 46, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 32, 4, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 32, 29, 1] -8\n", - "[18, 64, 58, 2] -4\n", - "[27, 96, 87, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 33, 9, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 33, 44, 1] -8\n", - "[18, 66, 88, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 34, 47, 1] -8\n", - "[18, 68, 94, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 36, 17, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 36, 44, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 37, 19, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 38, 5, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 41, 40, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 41, 46, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 42, 6, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 43, 11, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 43, 29, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 44, 1, 0] -139\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 44, 38, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 45, 20, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 46, 39, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 47, 45, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 48, 24, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 48, 36, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 49, 40, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 50, 16, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[9, 51, 7, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 0, 2, 1] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 1, 2, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 2, 25, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 2, 27, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 3, 42, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 4, 15, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 5, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 5, 50, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 7, 19, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 8, 45, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 10, 0, 0] -4\n", - "[20, 20, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 10, 1, 1] -4\n", - "[20, 20, 2, 2] -8\n", - "[30, 30, 3, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 14, 32, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 15, 34, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 18, 11, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 18, 15, 1] 0\n", - "[20, 36, 30, 2] 0\n", - "[30, 54, 45, 3] 0\n", - "[40, 72, 60, 4] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 19, 40, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 19, 46, 1] 8\n", - "[20, 38, 92, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 21, 41, 1] 8\n", - "[20, 42, 82, 2] -8\n", - "[30, 63, 123, 3] -4\n", - "[40, 84, 164, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 21, 49, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 22, 30, 1] 4\n", - "[20, 44, 60, 2] 0\n", - "[30, 66, 90, 3] -8\n", - "[40, 88, 120, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 23, 11, 1] -8\n", - "[20, 46, 22, 2] -8\n", - "[30, 69, 33, 3] 8\n", - "[40, 92, 44, 4] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 23, 29, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 24, 8, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 26, 24, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 28, 13, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 30, 39, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 31, 48, 1] -4\n", - "[20, 62, 96, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 32, 10, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 33, 28, 1] -8\n", - "[20, 66, 56, 2] 0\n", - "[30, 99, 84, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 34, 51, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 36, 8, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 36, 28, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 37, 31, 1] -8\n", - "[20, 74, 62, 2] 8\n", - "[30, 111, 93, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 37, 41, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 39, 17, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 39, 44, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 40, 26, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 40, 33, 1] -8\n", - "[20, 80, 66, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 41, 6, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 42, 4, 0] -135\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 42, 29, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 45, 22, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 46, 33, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 46, 36, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 47, 7, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 47, 16, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 48, 12, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 49, 6, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 50, 49, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 51, 21, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[10, 51, 37, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 5, 25, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 5, 27, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 6, 11, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 6, 15, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 7, 49, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 8, 47, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 9, 8, 1] 8\n", - "[22, 18, 16, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 9, 28, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 10, 17, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 10, 44, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 11, 0, 0] -4\n", - "[22, 22, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 11, 1, 1] -4\n", - "[22, 22, 2, 2] -8\n", - "[33, 33, 3, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 12, 34, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 13, 7, 1] 0\n", - "[22, 26, 14, 2] 0\n", - "[33, 39, 21, 3] -4\n", - "[44, 52, 28, 4] 0\n", - "[55, 65, 35, 5] 8\n", - "[66, 78, 42, 6] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 14, 30, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 15, 1, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 15, 38, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 16, 41, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 16, 49, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 17, 13, 1] 0\n", - "[22, 34, 26, 2] 4\n", - "[33, 51, 39, 3] 0\n", - "[44, 68, 52, 4] 8\n", - "[55, 85, 65, 5] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 18, 10, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 19, 31, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 22, 40, 1] 8\n", - "[22, 44, 80, 2] -4\n", - "[33, 66, 120, 3] -4\n", - "[44, 88, 160, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 23, 10, 1] -8\n", - "[22, 46, 20, 2] -8\n", - "[33, 69, 30, 3] 4\n", - "[44, 92, 40, 4] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 25, 14, 1] -8\n", - "[22, 50, 28, 2] -4\n", - "[33, 75, 42, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 25, 35, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 26, 12, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 27, 14, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 28, 47, 1] 0\n", - "[22, 56, 94, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 29, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 30, 26, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 30, 33, 1] 0\n", - "[22, 60, 66, 2] 0\n", - "[33, 90, 99, 3] 4\n", - "[44, 120, 132, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 31, 4, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 31, 29, 1] -4\n", - "[22, 62, 58, 2] 0\n", - "[33, 93, 87, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 32, 39, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 33, 12, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 37, 42, 1] -4\n", - "[22, 74, 84, 2] 4\n", - "[33, 111, 126, 3] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 39, 24, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 40, 48, 1] -8\n", - "[22, 80, 96, 2] -4\n", - "[33, 120, 144, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 41, 4, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 41, 18, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 42, 43, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 43, 9, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 44, 8, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 45, 16, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 46, 48, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 47, 21, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 47, 50, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 49, 18, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 49, 23, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 51, 3, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[11, 51, 27, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 0, 28, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 1, 8, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 1, 28, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 2, 13, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 3, 22, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 4, 39, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 6, 43, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 7, 3, 1] 8\n", - "[24, 14, 6, 2] 4\n", - "[36, 21, 9, 3] 4\n", - "[48, 28, 12, 4] 0\n", - "[60, 35, 15, 5] -4\n", - "[72, 42, 18, 6] -4\n", - "[84, 49, 21, 7] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 7, 27, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 8, 34, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 9, 12, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 10, 33, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 10, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 11, 9, 1] 8\n", - "[24, 22, 18, 2] 8\n", - "[36, 33, 27, 3] 8\n", - "[48, 44, 36, 4] 4\n", - "[60, 55, 45, 5] 0\n", - "[72, 66, 54, 6] 4\n", - "[84, 77, 63, 7] 4\n", - "[96, 88, 72, 8] 0\n", - "[108, 99, 81, 9] 8\n", - "[120, 110, 90, 10] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 12, 0, 0] -4\n", - "[24, 24, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 12, 1, 1] -4\n", - "[24, 24, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 13, 5, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 13, 51, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 14, 19, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 15, 9, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 15, 44, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 16, 3, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 20, 16, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 21, 20, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 21, 35, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 22, 49, 1] 8\n", - "[24, 44, 98, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 23, 30, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 26, 11, 1] -8\n", - "[24, 52, 22, 2] -8\n", - "[36, 78, 33, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 26, 29, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 28, 34, 1] 4\n", - "[24, 56, 68, 2] 0\n", - "[36, 84, 102, 3] -4\n", - "[48, 112, 136, 4] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 29, 39, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 30, 6, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 31, 32, 1] 0\n", - "[24, 62, 64, 2] 0\n", - "[36, 93, 96, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 32, 46, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 33, 11, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 33, 15, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 35, 19, 1] -8\n", - "[24, 70, 38, 2] 4\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[36, 105, 57, 3] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 36, 15, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 37, 14, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 37, 35, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 38, 8, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 39, 48, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 40, 18, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 40, 23, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 42, 30, 1] -8\n", - "[24, 84, 60, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 43, 26, 1] -8\n", - "[24, 86, 52, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 44, 12, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 45, 50, 1] -8\n", - "[24, 90, 100, 2] 4\n", - "[36, 135, 150, 3] 8\n", - "[48, 180, 200, 4] -4\n", - "[60, 225, 250, 5] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 46, 4, 1] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 46, 18, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 48, 10, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[12, 50, 20, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 0, 48, 1] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 1, 48, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 2, 12, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 3, 47, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 5, 28, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 9, 4, 1] 4\n", - "[26, 18, 8, 2] 4\n", - "[39, 27, 12, 3] 0\n", - "[52, 36, 16, 4] 0\n", - "[65, 45, 20, 5] -4\n", - "[78, 54, 24, 6] -8\n", - "[91, 63, 28, 7] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 9, 18, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 10, 31, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 11, 40, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 11, 46, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 12, 39, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 13, 0, 0] -4\n", - "[26, 26, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 13, 1, 1] -4\n", - "[26, 26, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 14, 50, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 15, 46, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 17, 11, 1] 4\n", - "[26, 34, 22, 2] 0\n", - "[39, 51, 33, 3] 4\n", - "[52, 68, 44, 4] 8\n", - "[65, 85, 55, 5] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 17, 29, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 18, 19, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 20, 5, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 20, 51, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 21, 13, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 22, 25, 1] 8\n", - "[26, 44, 50, 2] 0\n", - "[39, 66, 75, 3] 4\n", - "[52, 88, 100, 4] 8\n", - "[65, 110, 125, 5] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 23, 19, 1] 4\n", - "[26, 46, 38, 2] 0\n", - "[39, 69, 57, 3] 8\n", - "[52, 92, 76, 4] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 24, 43, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 27, 47, 1] 4\n", - "[26, 54, 94, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 28, 10, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 29, 40, 1] 4\n", - "[26, 58, 80, 2] -4\n", - "[39, 87, 120, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 31, 22, 1] -4\n", - "[26, 62, 44, 2] 0\n", - "[39, 93, 66, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 32, 49, 1] 0\n", - "[26, 64, 98, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 33, 32, 1] 0\n", - "[26, 66, 64, 2] 4\n", - "[39, 99, 96, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 34, 24, 1] -4\n", - "[26, 68, 48, 2] 4\n", - "[39, 102, 72, 3] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 34, 36, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 35, 51, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 36, 32, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 36, 43, 1] 0\n", - "[26, 72, 86, 2] 0\n", - "[39, 108, 129, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 37, 45, 1] -4\n", - "[26, 74, 90, 2] -4\n", - "[39, 111, 135, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 39, 23, 1] -8\n", - "[26, 78, 46, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 39, 42, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 40, 14, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 40, 35, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 42, 16, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 43, 41, 1] -4\n", - "[26, 86, 82, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 43, 49, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 44, 4, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 44, 29, 1] -8\n", - "[26, 88, 58, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 45, 38, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 46, 14, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 47, 17, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 48, 30, 1] -8\n", - "[26, 96, 60, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 50, 13, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 51, 8, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[13, 51, 28, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 2, 18, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 2, 23, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 3, 15, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 4, 51, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 5, 6, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 6, 47, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 7, 33, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 7, 36, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 9, 20, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 9, 35, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 10, 25, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 10, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 11, 21, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 11, 50, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 12, 19, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 13, 30, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 14, 0, 0] -4\n", - "[28, 28, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 14, 1, 1] -4\n", - "[28, 28, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 15, 21, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 15, 37, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 16, 24, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 16, 36, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 17, 14, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 18, 5, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 18, 51, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 19, 28, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 22, 17, 1] 4\n", - "[28, 44, 34, 2] 4\n", - "[42, 66, 51, 3] 8\n", - "[56, 88, 68, 4] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 22, 44, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 23, 5, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 24, 22, 1] 4\n", - "[28, 48, 44, 2] 0\n", - "[42, 72, 66, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 25, 11, 1] -4\n", - "[28, 50, 22, 2] -4\n", - "[42, 75, 33, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 25, 29, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 26, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 27, 11, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 27, 15, 1] -4\n", - "[28, 54, 30, 2] 0\n", - "[42, 81, 45, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 29, 50, 1] 4\n", - "[28, 58, 100, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 32, 2, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 34, 31, 1] 0\n", - "[28, 68, 62, 2] 8\n", - "[42, 102, 93, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 34, 41, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 35, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 37, 12, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 38, 42, 1] 0\n", - "[28, 76, 84, 2] 8\n", - "[42, 114, 126, 3] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 40, 13, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 42, 34, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 44, 14, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 44, 35, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 45, 39, 1] -4\n", - "[28, 90, 78, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 46, 13, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 47, 46, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 48, 7, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 50, 48, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[14, 51, 6, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 3, 14, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 4, 10, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 5, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 6, 11, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 6, 29, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 7, 37, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 8, 47, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 9, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 10, 9, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 10, 44, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 11, 0, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 12, 34, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 15, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 15, 1, 1] -8\n", - "[30, 30, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 16, 49, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 17, 8, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 18, 10, 1] 0\n", - "[30, 36, 20, 2] 0\n", - "[45, 54, 30, 3] 0\n", - "[60, 72, 40, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 19, 31, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 19, 41, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 20, 22, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 23, 43, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 25, 20, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 25, 35, 1] 8\n", - "[30, 50, 70, 2] 4\n", - "[45, 75, 105, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 27, 14, 1] -8\n", - "[30, 54, 28, 2] 0\n", - "[45, 81, 42, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 27, 35, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 30, 26, 1] 0\n", - "[30, 60, 52, 2] 4\n", - "[45, 90, 78, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 31, 4, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 31, 18, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 32, 39, 1] 0\n", - "[30, 64, 78, 2] 4\n", - "[45, 96, 117, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 33, 12, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 34, 2, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 36, 12, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 39, 24, 1] -8\n", - "[30, 78, 48, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 39, 36, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 40, 6, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 41, 18, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 41, 23, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 42, 32, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 42, 43, 1] -4\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[30, 84, 86, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 43, 39, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 44, 8, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 44, 28, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 45, 7, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 45, 16, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 46, 48, 1] -8\n", - "[30, 92, 96, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 47, 50, 1] -8\n", - "[30, 94, 100, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 48, 15, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 49, 23, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 49, 42, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 50, 3, 0] -131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 51, 25, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[15, 51, 27, 1] -8\n", - "[30, 102, 54, 2] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 1, 40, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 2, 26, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 3, 28, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 5, 39, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 7, 0, 1] 107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 8, 18, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 8, 23, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 9, 49, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 10, 16, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 11, 22, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 13, 4, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 13, 29, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 15, 22, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 16, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 16, 1, 1] -8\n", - "[32, 32, 2, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 17, 31, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 17, 41, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 18, 45, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 19, 38, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 20, 12, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 21, 17, 1] 4\n", - "[32, 42, 34, 2] 8\n", - "[48, 63, 51, 3] 4\n", - "[64, 84, 68, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 21, 44, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 22, 34, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 23, 45, 1] 8\n", - "[32, 46, 90, 2] -8\n", - "[48, 69, 135, 3] 8\n", - "[64, 92, 180, 4] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 25, 24, 1] 4\n", - "[32, 50, 48, 2] 4\n", - "[48, 75, 72, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 25, 36, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 26, 3, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 26, 27, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 27, 24, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 28, 23, 1] 0\n", - "[32, 56, 46, 2] 4\n", - "[48, 84, 69, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 28, 42, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 30, 51, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 33, 3, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 34, 30, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 37, 17, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 38, 40, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 38, 46, 1] -4\n", - "[32, 76, 92, 2] 4\n", - "[48, 114, 138, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 39, 21, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 39, 37, 1] -4\n", - "[32, 78, 74, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 42, 13, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 43, 7, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 44, 41, 1] -4\n", - "[32, 88, 82, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 44, 49, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 45, 11, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 45, 15, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 46, 25, 1] -8\n", - "[32, 92, 50, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 47, 10, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 48, 20, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 48, 35, 1] -4\n", - "[32, 96, 70, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 50, 9, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 50, 44, 1] -8\n", - "[32, 100, 88, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[16, 51, 39, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 2, 5, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 3, 21, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 3, 37, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 4, 6, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 5, 47, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 6, 46, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 10, 11, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 10, 29, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 11, 48, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 12, 24, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 17, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 17, 1, 1] -8\n", - "[34, 34, 2, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 18, 6, 1] -4\n", - "[34, 36, 12, 2] -8\n", - "[51, 54, 18, 3] -4\n", - "[68, 72, 24, 4] 8\n", - "[85, 90, 30, 5] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 19, 22, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 20, 3, 1] -8\n", - "[34, 40, 6, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 20, 27, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 21, 7, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 21, 16, 1] 4\n", - "[34, 42, 32, 2] 4\n", - "[51, 63, 48, 3] 4\n", - "[68, 84, 64, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 22, 14, 1] 0\n", - "[34, 44, 28, 2] 0\n", - "[51, 66, 42, 3] 8\n", - "[68, 88, 56, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 22, 35, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 23, 31, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 24, 9, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 24, 44, 1] 8\n", - "[34, 48, 88, 2] -8\n", - "[51, 72, 132, 3] 8\n", - "[68, 96, 176, 4] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 25, 50, 1] 8\n", - "[34, 50, 100, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 26, 39, 1] 8\n", - "[34, 52, 78, 2] 0\n", - "[51, 78, 117, 3] 4\n", - "[68, 104, 156, 4] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 27, 21, 1] 0\n", - "[34, 54, 42, 2] 4\n", - "[51, 81, 63, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 27, 50, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 28, 17, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 29, 48, 1] 4\n", - "[34, 58, 96, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 30, 32, 1] 4\n", - "[34, 60, 64, 2] 4\n", - "[51, 90, 96, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 31, 40, 1] 4\n", - "[34, 62, 80, 2] 0\n", - "[51, 93, 120, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 32, 18, 1] -4\n", - "[34, 64, 36, 2] 4\n", - "[51, 96, 54, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 32, 23, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 33, 39, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 35, 3, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 36, 9, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 37, 16, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 38, 34, 1] 0\n", - "[34, 76, 68, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 39, 10, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 40, 30, 1] -4\n", - "[34, 80, 60, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 42, 31, 1] -4\n", - "[34, 84, 62, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 42, 41, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 43, 4, 1] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 43, 18, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 44, 0, 1] 71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 46, 30, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 47, 13, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 48, 26, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 48, 33, 1] -4\n", - "[34, 96, 66, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 49, 19, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 50, 7, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[17, 51, 47, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 2, 14, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 2, 35, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 3, 32, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 3, 43, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 4, 1, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 4, 38, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 7, 31, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 8, 7, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 8, 16, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 9, 13, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 11, 2, 1] 4\n", - "[36, 22, 4, 2] -4\n", - "[54, 33, 6, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 12, 51, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 13, 19, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 14, 39, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 15, 2, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[18, 16, 6, 1] 0\n", - "[36, 32, 12, 2] -4\n", - "[54, 48, 18, 3] -4\n", - "[72, 64, 24, 4] 4\n", - "[90, 80, 30, 5] 4\n", - "[108, 96, 36, 6] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 17, 45, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 18, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 18, 1, 1] -8\n", - "[36, 36, 2, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 19, 48, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 20, 30, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 21, 18, 1] 8\n", - "[36, 42, 36, 2] 4\n", - "[54, 63, 54, 3] 4\n", - "[72, 84, 72, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 21, 23, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 22, 26, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 23, 0, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 24, 47, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 27, 32, 1] 8\n", - "[36, 54, 64, 2] 4\n", - "[54, 81, 96, 3] 0\n", - "[72, 108, 128, 4] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 28, 7, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 29, 38, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 30, 24, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 31, 15, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 32, 17, 1] -4\n", - "[36, 64, 34, 2] 8\n", - "[54, 96, 51, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 32, 44, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 34, 3, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 34, 27, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 36, 47, 1] 0\n", - "[36, 72, 94, 2] -4\n", - "[54, 108, 141, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 37, 4, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 37, 18, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 38, 20, 1] -8\n", - "[36, 76, 40, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 39, 8, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 40, 12, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 41, 11, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 41, 15, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 43, 17, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 44, 45, 1] -4\n", - "[36, 88, 90, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 46, 12, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 47, 49, 1] -4\n", - "[36, 94, 98, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 48, 34, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 49, 11, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 49, 29, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 50, 23, 1] -8\n", - "[36, 100, 46, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[18, 50, 42, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 0, 19, 1] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 1, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 2, 40, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 2, 46, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 3, 24, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 3, 36, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 4, 45, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 5, 30, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 7, 10, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 8, 42, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 9, 21, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 9, 37, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 10, 7, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 12, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 12, 35, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 13, 18, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 13, 23, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 14, 12, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 17, 49, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 18, 13, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 19, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 19, 1, 1] -8\n", - "[38, 38, 2, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 21, 9, 1] 0\n", - "[38, 42, 18, 2] 0\n", - "[57, 63, 27, 3] 4\n", - "[76, 84, 36, 4] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 23, 13, 1] 0\n", - "[38, 46, 26, 2] 4\n", - "[57, 69, 39, 3] 8\n", - "[76, 92, 52, 4] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 24, 3, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 25, 26, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 25, 33, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 26, 25, 1] 8\n", - "[38, 52, 50, 2] 4\n", - "[57, 78, 75, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 27, 33, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 27, 36, 1] 8\n", - "[38, 54, 72, 2] 4\n", - "[57, 81, 108, 3] -4\n", - "[76, 108, 144, 4] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 29, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 30, 5, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 32, 47, 1] 4\n", - "[38, 64, 94, 2] -8\n", - "[57, 96, 141, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 33, 25, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 33, 27, 1] 4\n", - "[38, 66, 54, 2] 8\n", - "[57, 99, 81, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 35, 12, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 36, 3, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 36, 27, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 37, 9, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 37, 44, 1] 0\n", - "[38, 74, 88, 2] 4\n", - "[57, 111, 132, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 39, 50, 1] 0\n", - "[38, 78, 100, 2] -4\n", - "[57, 117, 150, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 40, 2, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 42, 8, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 43, 47, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 44, 37, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 45, 4, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 45, 29, 1] -4\n", - "[38, 90, 58, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 46, 2, 0] -127\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 47, 32, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 47, 43, 1] 0\n", - "[38, 94, 86, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 49, 17, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[19, 50, 39, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 0, 42, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 1, 23, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 1, 42, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 2, 4, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 2, 29, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 4, 21, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 4, 50, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 5, 48, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 6, 7, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 7, 24, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 8, 30, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 9, 14, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 10, 3, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 11, 37, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 13, 39, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 14, 38, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 15, 49, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 16, 28, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 18, 50, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 19, 8, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 20, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 20, 1, 1] -8\n", - "[40, 40, 2, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 21, 12, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 23, 51, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 25, 15, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 28, 30, 1] 8\n", - "[40, 56, 60, 2] 8\n", - "[60, 84, 90, 3] 8\n", - "[80, 112, 120, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 29, 21, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 29, 37, 1] 8\n", - "[40, 58, 74, 2] 4\n", - "[60, 87, 111, 3] 8\n", - "[80, 116, 148, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 31, 47, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 32, 25, 1] 4\n", - "[40, 64, 50, 2] 8\n", - "[60, 96, 75, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 33, 22, 1] 0\n", - "[40, 66, 44, 2] 8\n", - "[60, 99, 66, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 34, 6, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 35, 1, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 35, 38, 1] 4\n", - "[40, 70, 76, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 36, 22, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 38, 18, 1] -4\n", - "[40, 76, 36, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 38, 23, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 39, 20, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 39, 35, 1] 4\n", - "[40, 78, 70, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 40, 45, 1] 0\n", - "[40, 80, 90, 2] 8\n", - "[60, 120, 135, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 41, 47, 1] 0\n", - "[40, 82, 94, 2] 8\n", - "[60, 123, 141, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 42, 5, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 42, 51, 1] 0\n", - "[40, 84, 102, 2] 0\n", - "[60, 126, 153, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 43, 25, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[20, 43, 27, 1] 0\n", - "[40, 86, 54, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 45, 9, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 46, 45, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 47, 26, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 47, 33, 1] 0\n", - "[40, 94, 66, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 48, 16, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 50, 12, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[20, 51, 48, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 1, 30, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 2, 39, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 3, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 4, 20, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 5, 10, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 6, 25, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 6, 27, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 8, 6, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 9, 19, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 10, 22, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 11, 14, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 11, 35, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 12, 42, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 13, 48, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 14, 8, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 15, 14, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 17, 40, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 19, 34, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 20, 28, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 21, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 21, 1, 1] -8\n", - "[42, 42, 2, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 24, 41, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 24, 49, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 25, 9, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 25, 44, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 26, 21, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 26, 37, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 27, 17, 1] 4\n", - "[42, 54, 34, 2] 8\n", - "[63, 81, 51, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 27, 44, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 28, 31, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 29, 20, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 29, 35, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 32, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 33, 37, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 34, 32, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 34, 43, 1] 8\n", - "[42, 68, 86, 2] 4\n", - "[63, 102, 129, 3] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 35, 8, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 35, 28, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 36, 49, 1] 4\n", - "[42, 72, 98, 2] -8\n", - "[63, 108, 147, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 37, 1, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 37, 38, 1] 4\n", - "[42, 74, 76, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 38, 30, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 39, 16, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 40, 51, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 41, 2, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 46, 50, 1] 0\n", - "[42, 92, 100, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 47, 11, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 47, 29, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 48, 3, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 49, 2, 1] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 50, 0, 1] 75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[21, 51, 10, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 0, 49, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 1, 41, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 1, 49, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 2, 6, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 3, 12, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 5, 46, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 6, 45, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 7, 9, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 9, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 10, 21, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 10, 50, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 11, 7, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 11, 16, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 12, 22, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 13, 32, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 13, 43, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 15, 16, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 16, 9, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 16, 44, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 18, 47, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 19, 17, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 20, 15, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 21, 24, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 21, 36, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 22, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 22, 1, 1] -8\n", - "[44, 44, 2, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 23, 47, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 24, 14, 1] 4\n", - "[44, 48, 28, 2] 0\n", - "[66, 72, 42, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 24, 35, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 25, 48, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 29, 7, 1] -8\n", - "[44, 58, 14, 2] -8\n", - "[66, 87, 21, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 30, 2, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 31, 13, 1] -4\n", - "[44, 62, 26, 2] 4\n", - "[66, 93, 39, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 32, 5, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 32, 51, 1] 8\n", - "[44, 64, 102, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 33, 20, 1] 0\n", - "[44, 66, 40, 2] 8\n", - "[66, 99, 60, 3] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 34, 40, 1] 8\n", - "[44, 68, 80, 2] 4\n", - "[66, 102, 120, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 36, 20, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 36, 35, 1] 8\n", - "[44, 72, 70, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 37, 24, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 38, 31, 1] 4\n", - "[44, 76, 62, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 38, 41, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 39, 25, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 39, 27, 1] 4\n", - "[44, 78, 54, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 41, 8, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 43, 51, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 45, 10, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 49, 8, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 49, 28, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 50, 33, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 50, 36, 1] 0\n", - "[44, 100, 72, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[22, 51, 26, 1] 0\n", - "[44, 102, 52, 2] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 1, 20, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 2, 14, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 3, 43, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 4, 38, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 6, 34, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[23, 7, 6, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 8, 16, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 9, 45, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 11, 2, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 12, 50, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 13, 19, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 14, 39, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 16, 6, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 18, 1, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 18, 38, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 19, 48, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 21, 4, 1] -4\n", - "[46, 42, 8, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 21, 18, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 22, 26, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 22, 33, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 23, 0, 0] -8\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 23, 1, 1] -8\n", - "[46, 46, 2, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 25, 32, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 27, 32, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 27, 43, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 28, 7, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 28, 16, 1] 4\n", - "[46, 56, 32, 2] 4\n", - "[69, 84, 48, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 29, 2, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 30, 28, 1] 8\n", - "[46, 60, 56, 2] 4\n", - "[69, 90, 84, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 32, 17, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 33, 47, 1] 8\n", - "[46, 66, 94, 2] -8\n", - "[69, 99, 141, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 34, 3, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 35, 39, 1] 8\n", - "[46, 70, 78, 2] 8\n", - "[69, 105, 117, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 36, 47, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 37, 4, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 37, 29, 1] 4\n", - "[46, 74, 58, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 38, 20, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 38, 35, 1] 8\n", - "[46, 76, 70, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 39, 13, 1] -8\n", - "[46, 78, 26, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 40, 12, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 41, 15, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 42, 0, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 44, 45, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 45, 40, 1] 4\n", - "[46, 90, 80, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 47, 41, 1] 4\n", - "[46, 94, 82, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 47, 49, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 48, 5, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 49, 11, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 49, 15, 1] -8\n", - "[46, 98, 30, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 50, 18, 1] -4\n", - "[46, 100, 36, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 50, 23, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[23, 51, 42, 1] 4\n", - "[46, 102, 84, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 2, 47, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 3, 19, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 4, 26, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 4, 33, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 5, 45, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 6, 39, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 7, 20, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 7, 35, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 8, 2, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 11, 24, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 11, 36, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 12, 17, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 14, 41, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 14, 49, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 15, 24, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 16, 14, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 16, 35, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 17, 34, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 18, 26, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 20, 37, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 21, 22, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 23, 46, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 24, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 24, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 25, 7, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 25, 16, 1] 4\n", - "[48, 50, 32, 2] 4\n", - "[72, 75, 48, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 26, 10, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 27, 16, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 28, 38, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 29, 33, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 29, 36, 1] 8\n", - "[48, 58, 72, 2] 4\n", - "[72, 87, 108, 3] 4\n", - "[96, 116, 144, 4] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 30, 4, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 30, 18, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 31, 30, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 32, 6, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 34, 13, 1] -8\n", - "[48, 68, 26, 2] 8\n", - "[72, 102, 39, 3] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 35, 49, 1] 4\n", - "[48, 70, 98, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 36, 0, 1] 79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 37, 22, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 39, 11, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 39, 15, 1] -8\n", - "[48, 78, 30, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 40, 32, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 40, 43, 1] 4\n", - "[48, 80, 86, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 41, 30, 1] 0\n", - "[48, 82, 60, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 42, 40, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 42, 46, 1] 0\n", - "[48, 84, 92, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 43, 48, 1] 0\n", - "[48, 86, 96, 2] 8\n", - "[72, 129, 144, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 45, 25, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 45, 27, 1] 0\n", - "[48, 90, 54, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 46, 43, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 48, 9, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[24, 51, 45, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 0, 32, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 1, 32, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 1, 43, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 2, 10, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 3, 38, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 4, 3, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 5, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 5, 15, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 6, 21, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 6, 37, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 8, 26, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 10, 14, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 12, 31, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 13, 33, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 13, 36, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 15, 42, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 17, 30, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 18, 3, 1] 0\n", - "[50, 36, 6, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 18, 27, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 19, 47, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 21, 34, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 22, 13, 1] 4\n", - "[50, 44, 26, 2] 4\n", - "[75, 66, 39, 3] 4\n", - "[100, 88, 52, 4] 4\n", - "[125, 110, 65, 5] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 23, 25, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 23, 27, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 24, 40, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 25, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 25, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 26, 19, 1] 8\n", - "[50, 52, 38, 2] 4\n", - "[75, 78, 57, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 27, 1, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 27, 38, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 28, 46, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 31, 50, 1] 8\n", - "[50, 62, 100, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 32, 20, 1] 0\n", - "[50, 64, 40, 2] 8\n", - "[75, 96, 60, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 33, 19, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 34, 4, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 34, 29, 1] 4\n", - "[50, 68, 58, 2] 8\n", - "[75, 102, 87, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 37, 34, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 38, 43, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 39, 22, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 40, 7, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 41, 51, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 42, 25, 1] 0\n", - "[50, 84, 50, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 43, 20, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 43, 35, 1] 4\n", - "[50, 86, 70, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 44, 30, 1] 0\n", - "[50, 88, 60, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 45, 24, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 46, 7, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 46, 16, 1] -8\n", - "[50, 92, 32, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 48, 49, 1] 0\n", - "[50, 96, 98, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 49, 5, 0] -123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 49, 51, 1] 0\n", - "[50, 98, 102, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[25, 51, 15, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 0, 47, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 1, 47, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 2, 7, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 2, 16, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 3, 40, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 4, 24, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 6, 9, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 6, 44, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 8, 25, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 9, 34, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 11, 8, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 11, 28, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[26, 13, 3, 1] 8\n", - "[52, 26, 6, 2] -4\n", - "[78, 39, 9, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 13, 27, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 14, 6, 1] 8\n", - "[52, 28, 12, 2] 0\n", - "[78, 42, 18, 3] -8\n", - "[104, 56, 24, 4] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 15, 8, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 17, 5, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 17, 51, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 18, 24, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 18, 36, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 19, 32, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 19, 43, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 20, 31, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 20, 41, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 22, 18, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 22, 23, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 23, 33, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 23, 36, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 24, 2, 1] -8\n", - "[52, 48, 4, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 25, 19, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 26, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 26, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 29, 28, 1] 8\n", - "[52, 58, 56, 2] 4\n", - "[78, 87, 84, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 30, 11, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 30, 15, 1] 0\n", - "[52, 60, 30, 2] 4\n", - "[78, 90, 45, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 31, 39, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 33, 1, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 33, 38, 1] 8\n", - "[52, 66, 76, 2] 8\n", - "[78, 99, 114, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 34, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 35, 31, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 36, 38, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 37, 30, 1] 4\n", - "[52, 74, 60, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 40, 10, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 41, 39, 1] 4\n", - "[52, 82, 78, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 42, 26, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 42, 33, 1] 4\n", - "[52, 84, 66, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 43, 12, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 44, 5, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 47, 20, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 47, 35, 1] 4\n", - "[52, 94, 70, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 48, 17, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[26, 51, 22, 1] -4\n", - "[52, 102, 44, 2] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 1, 32, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 2, 10, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 3, 1, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 3, 38, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 4, 3, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 4, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 5, 11, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 5, 29, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 6, 21, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 6, 50, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 7, 12, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 8, 46, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 10, 14, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 10, 35, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 12, 31, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 12, 41, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 13, 26, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 13, 33, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 17, 30, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 18, 25, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 18, 27, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 20, 17, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 22, 8, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 23, 25, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 25, 0, 1] 91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 26, 16, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 27, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 27, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 28, 40, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 28, 46, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 29, 3, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 30, 45, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 31, 51, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 33, 19, 1] 4\n", - "[54, 66, 38, 2] 8\n", - "[81, 99, 57, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 34, 4, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 34, 18, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 36, 19, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 37, 34, 1] 8\n", - "[54, 74, 68, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 38, 32, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 38, 43, 1] 8\n", - "[54, 76, 86, 2] 8\n", - "[81, 114, 129, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 39, 22, 1] 0\n", - "[54, 78, 44, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 41, 5, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 41, 51, 1] 4\n", - "[54, 82, 102, 2] -4\n", - "[81, 123, 153, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 43, 20, 1] -4\n", - "[54, 86, 40, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 45, 24, 1] 0\n", - "[54, 90, 48, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 45, 36, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 46, 7, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 47, 48, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 48, 37, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 49, 5, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 51, 11, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[27, 51, 15, 1] -8\n", - "[54, 102, 30, 2] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 0, 12, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 1, 12, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 3, 7, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 3, 16, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 4, 46, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 5, 13, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 6, 30, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 8, 1, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 8, 38, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 9, 11, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 9, 15, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 10, 48, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 11, 26, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 11, 33, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 12, 9, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 12, 44, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 13, 2, 1] 8\n", - "[56, 26, 4, 2] -8\n", - "[84, 39, 6, 3] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 14, 37, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 15, 33, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 15, 36, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 16, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 18, 40, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 18, 46, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 19, 14, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 19, 35, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 20, 21, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 20, 50, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 22, 3, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 23, 40, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 26, 43, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 27, 7, 1] -4\n", - "[56, 54, 14, 2] -8\n", - "[84, 81, 21, 3] 4\n", - "[112, 108, 28, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 28, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 28, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 29, 26, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 30, 23, 1] 8\n", - "[56, 60, 46, 2] 4\n", - "[84, 90, 69, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 30, 42, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 32, 31, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 33, 10, 1] -4\n", - "[56, 66, 20, 2] 0\n", - "[84, 99, 30, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 34, 8, 1] -8\n", - "[56, 68, 16, 2] 0\n", - "[84, 102, 24, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 34, 28, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 35, 21, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 35, 37, 1] 8\n", - "[56, 70, 74, 2] 8\n", - "[84, 105, 111, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 36, 10, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 39, 4, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 39, 29, 1] 4\n", - "[56, 78, 58, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 43, 6, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 44, 15, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 46, 32, 1] 4\n", - "[56, 92, 64, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 48, 39, 1] 4\n", - "[56, 96, 78, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 49, 22, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 50, 45, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[28, 51, 13, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 2, 20, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 4, 0, 1] 123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 5, 3, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 5, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 6, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 7, 41, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 7, 49, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 9, 8, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 10, 17, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 11, 1, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 11, 38, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 12, 5, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 13, 7, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 13, 16, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 14, 30, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 15, 38, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 16, 31, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 16, 41, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 17, 13, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[29, 19, 6, 1] 4\n", - "[58, 38, 12, 2] -8\n", - "[87, 57, 18, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 21, 42, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 22, 40, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 22, 46, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 23, 10, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 25, 14, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 26, 12, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 28, 47, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 29, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 29, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 30, 33, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 30, 36, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 31, 11, 1] 0\n", - "[58, 62, 22, 2] 0\n", - "[87, 93, 33, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 31, 29, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 32, 9, 1] -4\n", - "[58, 64, 18, 2] 0\n", - "[87, 96, 27, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 34, 25, 1] 8\n", - "[58, 68, 50, 2] 8\n", - "[87, 102, 75, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 35, 30, 1] 8\n", - "[58, 70, 60, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 37, 23, 1] 4\n", - "[58, 74, 46, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 37, 42, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 39, 28, 1] 4\n", - "[58, 78, 56, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 40, 48, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 41, 4, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 41, 29, 1] 4\n", - "[58, 82, 58, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 42, 10, 1] -8\n", - "[58, 84, 20, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 43, 9, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 43, 44, 1] 4\n", - "[58, 86, 88, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 44, 13, 1] -8\n", - "[58, 88, 26, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 45, 19, 1] 0\n", - "[58, 90, 38, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 47, 21, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 47, 37, 1] 4\n", - "[58, 94, 74, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 49, 4, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 49, 18, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[29, 51, 3, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 0, 50, 1] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 1, 21, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 1, 50, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 2, 49, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 3, 6, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 5, 19, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 6, 8, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 6, 28, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 7, 30, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 8, 20, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 8, 35, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 10, 5, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 11, 47, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 12, 45, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 13, 14, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 14, 11, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 14, 29, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 15, 47, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 17, 25, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 17, 27, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 19, 39, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 20, 4, 1] 0\n", - "[60, 40, 8, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 20, 18, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 21, 46, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 22, 10, 1] 8\n", - "[60, 44, 20, 2] -4\n", - "[90, 66, 30, 3] -8\n", - "[120, 88, 40, 4] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 23, 12, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 25, 31, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 27, 6, 1] -4\n", - "[60, 54, 12, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 28, 20, 1] 8\n", - "[60, 56, 40, 2] 4\n", - "[90, 84, 60, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 30, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 30, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 31, 24, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 34, 16, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 35, 4, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 35, 29, 1] 8\n", - "[60, 70, 58, 2] 8\n", - "[90, 105, 87, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 37, 26, 1] 8\n", - "[60, 74, 52, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 38, 21, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 38, 37, 1] 8\n", - "[60, 76, 74, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 39, 2, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 40, 17, 1] 0\n", - "[60, 80, 34, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 40, 44, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 41, 24, 1] 4\n", - "[60, 82, 48, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 41, 36, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 42, 12, 1] -8\n", - "[60, 84, 24, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 43, 34, 1] 8\n", - "[60, 86, 68, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 44, 25, 1] 4\n", - "[60, 88, 50, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 46, 17, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 48, 13, 1] -8\n", - "[60, 96, 26, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 49, 33, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 49, 36, 1] 4\n", - "[60, 98, 72, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 50, 40, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[30, 50, 46, 1] 4\n", - "[60, 100, 92, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 3, 39, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 6, 38, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 7, 4, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 7, 18, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 8, 37, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 10, 13, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 12, 25, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 12, 27, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 13, 41, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 13, 49, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 14, 33, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 14, 36, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 16, 4, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 16, 29, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 17, 7, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 17, 16, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 19, 11, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 19, 15, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 20, 26, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 21, 43, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 22, 48, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 23, 17, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 24, 50, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 25, 30, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 26, 5, 1] -4\n", - "[62, 52, 10, 2] -8\n", - "[93, 78, 15, 3] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 28, 21, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 28, 37, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 31, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 31, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 32, 8, 1] -4\n", - "[62, 64, 16, 2] 0\n", - "[93, 96, 24, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 32, 28, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 33, 5, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 33, 51, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 34, 14, 1] 0\n", - "[62, 68, 28, 2] 8\n", - "[93, 102, 42, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 34, 35, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 35, 26, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 35, 33, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 36, 51, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 37, 10, 1] -4\n", - "[62, 74, 20, 2] 8\n", - "[93, 111, 30, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 38, 22, 1] 4\n", - "[62, 76, 44, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 39, 47, 1] 8\n", - "[62, 78, 94, 2] 4\n", - "[93, 117, 141, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 41, 0, 1] 83\n", - "\n", - "**********\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 42, 17, 1] 0\n", - "[62, 84, 34, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 42, 44, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 43, 8, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 44, 7, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 45, 31, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 46, 34, 1] 8\n", - "[62, 92, 68, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 47, 42, 1] 8\n", - "[62, 94, 84, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 48, 2, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 50, 32, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[31, 50, 43, 1] 8\n", - "[62, 100, 86, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 0, 25, 1] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 1, 25, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 1, 27, 1] 56\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 3, 4, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 3, 18, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 4, 34, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 5, 49, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 7, 40, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 7, 46, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 10, 2, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 11, 5, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 13, 22, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 14, 10, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 15, 5, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 15, 51, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 16, 46, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 19, 26, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 19, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 20, 32, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 20, 43, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 21, 6, 1] 4\n", - "[64, 42, 12, 2] -8\n", - "[96, 63, 18, 3] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 22, 39, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 24, 45, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 25, 23, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 25, 42, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 26, 8, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 27, 18, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 27, 23, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 29, 34, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 30, 17, 1] 8\n", - "[64, 60, 34, 2] 8\n", - "[96, 90, 51, 3] 8\n", - "[128, 120, 68, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 30, 44, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 31, 12, 1] 0\n", - "[64, 62, 24, 2] 4\n", - "[96, 93, 36, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 32, 0, 0] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 32, 1, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 33, 13, 1] 0\n", - "[64, 66, 26, 2] 8\n", - "[96, 99, 39, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 34, 21, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 34, 37, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 35, 43, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 36, 13, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 37, 6, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 38, 3, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 38, 27, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 40, 24, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 42, 15, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 43, 1, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 43, 38, 1] 8\n", - "[64, 86, 76, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 46, 28, 1] 4\n", - "[64, 92, 56, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 47, 19, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 49, 48, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 50, 31, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 51, 41, 1] 8\n", - "[64, 102, 82, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[32, 51, 49, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 1, 47, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 2, 7, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 4, 24, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 4, 36, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 6, 9, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 7, 14, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 9, 34, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 10, 12, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 11, 28, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 13, 25, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 13, 27, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 14, 31, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 15, 8, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 15, 28, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 17, 5, 1] 4\n", - "[66, 34, 10, 2] -4\n", - "[99, 51, 15, 3] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 18, 33, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 18, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 19, 32, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 20, 41, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 20, 49, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 22, 23, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 22, 42, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 23, 26, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 23, 33, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 24, 38, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 25, 19, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 26, 0, 1] 91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 27, 19, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 28, 2, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 29, 24, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 30, 11, 1] 0\n", - "[66, 60, 22, 2] 0\n", - "[99, 90, 33, 3] 8\n", - "[132, 120, 44, 4] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 30, 29, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 31, 39, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 32, 48, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 33, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 33, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 34, 45, 1] 8\n", - "[66, 68, 90, 2] -4\n", - "[99, 102, 135, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 35, 31, 1] 8\n", - "[66, 70, 62, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 35, 41, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 36, 1, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 36, 38, 1] 8\n", - "[66, 72, 76, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 38, 47, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 40, 10, 1] -8\n", - "[66, 80, 20, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 42, 26, 1] 4\n", - "[66, 84, 52, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 44, 34, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 45, 3, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 46, 10, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 47, 20, 1] -4\n", - "[66, 94, 40, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 48, 17, 1] -4\n", - "[66, 96, 34, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 48, 44, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 49, 30, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[33, 50, 22, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 0, 9, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 1, 9, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 1, 44, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 4, 32, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 5, 38, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 6, 23, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 6, 42, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 7, 51, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 8, 12, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 9, 26, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 9, 33, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 11, 43, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 12, 11, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 12, 15, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 15, 10, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 16, 50, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 17, 24, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 17, 36, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 19, 21, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 19, 37, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 20, 45, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 21, 25, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 22, 7, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 22, 16, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 24, 48, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 26, 6, 1] -4\n", - "[68, 52, 12, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 28, 12, 1] 0\n", - "[68, 56, 24, 2] 0\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[102, 84, 36, 3] -8\n", - "[136, 112, 48, 4] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 29, 32, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 29, 43, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 33, 6, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 34, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 34, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 36, 48, 1] 8\n", - "[68, 72, 96, 2] -8\n", - "[102, 108, 144, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 37, 25, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 37, 27, 1] 8\n", - "[68, 74, 54, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 38, 17, 1] 0\n", - "[68, 76, 34, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 38, 44, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 39, 46, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 40, 41, 1] 8\n", - "[68, 80, 82, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 40, 49, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 42, 14, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 43, 30, 1] 4\n", - "[68, 86, 60, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 44, 33, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 44, 36, 1] 4\n", - "[68, 88, 72, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 45, 47, 1] 4\n", - "[68, 90, 94, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 46, 31, 1] 4\n", - "[68, 92, 62, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 46, 41, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 47, 34, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 48, 4, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 48, 18, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 49, 3, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[34, 51, 2, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 1, 42, 1] 56\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 2, 4, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 2, 18, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 4, 50, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 5, 6, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 7, 24, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 7, 36, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 8, 30, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 9, 14, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 9, 35, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 10, 3, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 10, 27, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 11, 21, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 11, 37, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 12, 19, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 14, 1, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 14, 38, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 15, 37, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 16, 24, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 18, 51, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 19, 8, 1] 8\n", - "[70, 38, 16, 2] -4\n", - "[105, 57, 24, 3] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 19, 28, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 20, 0, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 21, 12, 1] 8\n", - "[70, 42, 24, 2] 0\n", - "[105, 63, 36, 3] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 22, 17, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 23, 5, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 23, 51, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 24, 22, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 25, 11, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 25, 15, 1] 8\n", - "[70, 50, 30, 2] 0\n", - "[105, 75, 45, 3] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 27, 15, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 29, 21, 1] 8\n", - "[70, 58, 42, 2] 4\n", - "[105, 87, 63, 3] 0\n", - "[140, 116, 84, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 29, 50, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 31, 47, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 34, 31, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 35, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 35, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 36, 22, 1] 4\n", - "[70, 72, 44, 2] 8\n", - "[105, 108, 66, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 37, 12, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 38, 23, 1] 4\n", - "[70, 76, 46, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 38, 42, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 39, 20, 1] 0\n", - "[70, 78, 40, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 40, 13, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 42, 5, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 43, 25, 1] 4\n", - "[70, 86, 50, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 44, 14, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 45, 39, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 46, 45, 1] 4\n", - "[70, 92, 90, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 47, 26, 1] 4\n", - "[70, 94, 52, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 48, 7, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 48, 16, 1] -4\n", - "[70, 96, 32, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[35, 51, 48, 1] 4\n", - "[70, 102, 96, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 3, 19, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 4, 33, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 4, 36, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 5, 45, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 6, 39, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 7, 14, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 7, 35, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 8, 2, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 10, 12, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 11, 24, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 13, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 14, 31, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 14, 41, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 15, 28, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 16, 14, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 17, 34, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 18, 26, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 18, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 20, 49, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 21, 22, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 22, 42, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 23, 26, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 24, 1, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 24, 38, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 25, 16, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 27, 19, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 28, 2, 1] -8\n", - "[72, 56, 4, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 29, 24, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 29, 36, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 30, 4, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 30, 29, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 32, 48, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 33, 0, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 34, 13, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 35, 41, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 35, 49, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 36, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 36, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 38, 47, 1] 8\n", - "[72, 76, 94, 2] 0\n", - "[108, 114, 141, 3] 8\n", - "[144, 152, 188, 4] 0\n", - "[180, 190, 235, 5] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 39, 15, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 40, 43, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 41, 30, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 42, 46, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 43, 48, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 44, 34, 1] 8\n", - "[72, 88, 68, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 45, 3, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 45, 27, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 46, 10, 1] -8\n", - "[72, 92, 20, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 48, 9, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 48, 44, 1] 4\n", - "[72, 96, 88, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 49, 30, 1] 4\n", - "[72, 98, 60, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[36, 50, 22, 1] 0\n", - "[72, 100, 44, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[37, 3, 17, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 3, 44, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 5, 43, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 6, 25, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 7, 15, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 8, 31, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 9, 19, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 11, 20, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 11, 35, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 13, 6, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 14, 8, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 14, 28, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 15, 14, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 15, 35, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 19, 34, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 20, 24, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 21, 0, 1] 99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 24, 49, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 25, 9, 1] 4\n", - "[74, 50, 18, 2] -4\n", - "[111, 75, 27, 3] -8\n", - "[148, 100, 36, 4] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 26, 21, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 26, 50, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 27, 9, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 27, 44, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 28, 31, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 28, 41, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 29, 20, 1] 8\n", - "[74, 58, 40, 2] 4\n", - "[111, 87, 60, 3] 8\n", - "[148, 116, 80, 4] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 30, 47, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 31, 2, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 32, 45, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 33, 21, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 33, 37, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 34, 32, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 35, 28, 1] 8\n", - "[74, 70, 56, 2] 8\n", - "[111, 105, 84, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 36, 37, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 37, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 37, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 38, 30, 1] 8\n", - "[74, 76, 60, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 39, 7, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 39, 16, 1] 0\n", - "[74, 78, 32, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 40, 5, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 40, 51, 1] 8\n", - "[74, 80, 102, 2] -8\n", - "[111, 120, 153, 3] 4\n", - "[148, 160, 204, 4] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 41, 2, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 43, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 44, 19, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 45, 48, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 46, 51, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 47, 4, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 47, 29, 1] 4\n", - "[74, 94, 58, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 48, 3, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 48, 27, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 49, 38, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[37, 51, 10, 1] -8\n", - "[74, 102, 20, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 1, 0, 1] 131\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 2, 38, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 3, 25, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 3, 27, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 4, 18, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 4, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 5, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 6, 31, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 8, 28, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 9, 39, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 10, 43, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 11, 4, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 11, 29, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 13, 8, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 14, 20, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 14, 35, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 15, 11, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 15, 29, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 16, 7, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 17, 9, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 17, 44, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 18, 23, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 18, 42, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 19, 16, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 21, 50, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 23, 42, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 24, 33, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 24, 36, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 26, 46, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 27, 25, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 28, 24, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 29, 4, 1] -8\n", - "[76, 58, 8, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 29, 18, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 31, 41, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 31, 49, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 33, 26, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 35, 20, 1] 4\n", - "[76, 70, 40, 2] 8\n", - "[114, 105, 60, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 36, 26, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 36, 33, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 37, 21, 1] 4\n", - "[76, 74, 42, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 37, 50, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 38, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 38, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 41, 49, 1] 8\n", - "[76, 82, 98, 2] -4\n", - "[114, 123, 147, 3] 4\n", - "[152, 164, 196, 4] -8\n", - "[190, 205, 245, 5] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 43, 32, 1] 8\n", - "[76, 86, 64, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 44, 9, 1] -8\n", - "[76, 88, 18, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 45, 13, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 46, 40, 1] 8\n", - "[76, 92, 80, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 48, 6, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 49, 37, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 50, 51, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[38, 51, 5, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 0, 5, 1] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 1, 5, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 1, 51, 1] 56\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 2, 21, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 2, 50, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 3, 31, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 3, 41, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 4, 12, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 5, 7, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 5, 16, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 6, 24, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 6, 36, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 9, 38, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 12, 13, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 13, 20, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 14, 18, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 14, 23, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 17, 2, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 19, 30, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 20, 42, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 22, 32, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 23, 48, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 25, 49, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 26, 17, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 26, 44, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 27, 41, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 27, 49, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 29, 12, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 30, 10, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 31, 26, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 31, 33, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 32, 11, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 32, 15, 1] 4\n", - "[78, 64, 30, 2] 0\n", - "[117, 96, 45, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 33, 17, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 35, 23, 1] 8\n", - "[78, 70, 46, 2] 4\n", - "[117, 105, 69, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 35, 42, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 37, 40, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 38, 51, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 39, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 39, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 40, 39, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 41, 26, 1] 8\n", - "[78, 82, 52, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 42, 48, 1] 8\n", - "[78, 84, 96, 2] 0\n", - "[117, 126, 144, 3] 8\n", - "[156, 168, 192, 4] -4\n", - "[195, 210, 240, 5] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 43, 15, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 44, 2, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 45, 14, 1] -4\n", - "[78, 90, 28, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 45, 35, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 46, 9, 1] -8\n", - "[78, 92, 18, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 48, 28, 1] 4\n", - "[78, 96, 56, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 49, 46, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 50, 19, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[39, 51, 16, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 0, 7, 1] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 1, 7, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 1, 16, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 2, 19, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[40, 3, 26, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 4, 8, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 7, 32, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 7, 43, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 8, 3, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 9, 51, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 10, 47, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 11, 13, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 14, 48, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 15, 45, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 16, 43, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 17, 21, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 17, 50, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 18, 8, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 18, 28, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 19, 10, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 20, 6, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 22, 11, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 22, 29, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 23, 28, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 24, 25, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 25, 40, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 25, 46, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 26, 2, 1] -4\n", - "[80, 52, 4, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 27, 46, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 28, 3, 1] -4\n", - "[80, 56, 6, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 28, 27, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 29, 13, 1] 4\n", - "[80, 58, 26, 2] 0\n", - "[120, 87, 39, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 31, 17, 1] 8\n", - "[80, 62, 34, 2] 4\n", - "[120, 93, 51, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 31, 44, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 33, 2, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 34, 22, 1] 8\n", - "[80, 68, 44, 2] 4\n", - "[120, 102, 66, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 35, 48, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 37, 39, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 38, 16, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 39, 5, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 40, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 40, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 41, 9, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 41, 44, 1] 8\n", - "[80, 82, 88, 2] 8\n", - "[120, 123, 132, 3] 8\n", - "[160, 164, 176, 4] 4\n", - "[200, 205, 220, 5] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 42, 24, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 44, 50, 1] 8\n", - "[80, 88, 100, 2] 4\n", - "[120, 132, 150, 3] 0\n", - "[160, 176, 200, 4] -8\n", - "[200, 220, 250, 5] 4\n", - "[240, 264, 300, 6] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 45, 23, 1] 4\n", - "[80, 90, 46, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 45, 42, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 46, 1, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 46, 38, 1] 8\n", - "[80, 92, 76, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 49, 9, 1] -8\n", - "[80, 98, 18, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[40, 50, 30, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 1, 22, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 3, 39, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 6, 2, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 7, 4, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 7, 29, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 8, 49, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 9, 7, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 10, 45, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 12, 3, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 12, 27, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 13, 31, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 13, 41, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 14, 24, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 14, 36, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 16, 11, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 16, 29, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 17, 16, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 19, 15, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 20, 26, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 20, 33, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 21, 10, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 24, 21, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 24, 50, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 26, 5, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 26, 51, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 27, 39, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 28, 37, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 31, 1, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 31, 38, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 32, 8, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 33, 51, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 34, 14, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 35, 33, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 35, 36, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 36, 50, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 37, 10, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 38, 22, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 39, 47, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 40, 34, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 41, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 41, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 42, 17, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 43, 13, 1] -4\n", - "[82, 86, 26, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 44, 7, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 44, 16, 1] 0\n", - "[82, 88, 32, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 45, 6, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 46, 34, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 47, 23, 1] 4\n", - "[82, 94, 46, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 47, 42, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 49, 0, 1] 83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 50, 43, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[41, 51, 32, 1] 8\n", - "[82, 102, 64, 2] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 0, 20, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 1, 20, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 1, 35, 1] 60\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 3, 10, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 4, 2, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 5, 42, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 6, 34, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 7, 6, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 8, 19, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 9, 45, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 12, 21, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 12, 50, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 14, 9, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 15, 25, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 16, 48, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 18, 38, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 20, 39, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 21, 4, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 21, 29, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 22, 33, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 22, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 23, 1, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 23, 38, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 24, 7, 1] 4\n", - "[84, 48, 14, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 25, 32, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 25, 43, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 26, 47, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 27, 43, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 28, 16, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 29, 2, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 30, 8, 1] 0\n", - "[84, 60, 16, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 30, 28, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 33, 47, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 35, 39, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 37, 11, 1] 0\n", - "[84, 74, 22, 2] 0\n", - "[126, 111, 33, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 37, 29, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 38, 14, 1] 0\n", - "[84, 76, 28, 2] 4\n", - "[126, 114, 42, 3] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 38, 35, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 39, 13, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 42, 0, 0] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 42, 1, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 45, 40, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[42, 45, 46, 1] 8\n", - "[84, 90, 92, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 47, 31, 1] 8\n", - "[84, 94, 62, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 47, 41, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 48, 5, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 48, 51, 1] 8\n", - "[84, 96, 102, 2] 8\n", - "[126, 144, 153, 3] 0\n", - "[168, 192, 204, 4] 8\n", - "[210, 240, 255, 5] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 49, 15, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 50, 4, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 50, 18, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 51, 23, 1] 4\n", - "[84, 102, 46, 2] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[42, 51, 42, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 1, 25, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 2, 3, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 3, 18, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 3, 23, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 5, 37, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 6, 12, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 7, 40, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 10, 38, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 11, 34, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 12, 47, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 13, 22, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 14, 43, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 15, 5, 1] 8\n", - "[86, 30, 10, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 16, 40, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 16, 46, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 19, 26, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 20, 32, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 21, 31, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 23, 15, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 24, 13, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 25, 42, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 26, 8, 1] 0\n", - "[86, 52, 16, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 26, 28, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 27, 23, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 27, 42, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 28, 45, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 29, 34, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 30, 9, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 30, 44, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 32, 0, 1] 87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 33, 8, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 34, 21, 1] 4\n", - "[86, 68, 42, 2] 0\n", - "[129, 102, 63, 3] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 34, 50, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 35, 32, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 35, 43, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 36, 13, 1] -4\n", - "[86, 72, 26, 2] 0\n", - "[129, 108, 39, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 37, 6, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 38, 25, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 38, 27, 1] 8\n", - "[86, 76, 54, 2] 4\n", - "[129, 114, 81, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 40, 24, 1] 4\n", - "[86, 80, 48, 2] 8\n", - "[129, 120, 72, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 40, 36, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 41, 48, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 42, 11, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 42, 15, 1] -4\n", - "[86, 84, 30, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 43, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 43, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 46, 24, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 47, 19, 1] 0\n", - "[86, 94, 38, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 49, 48, 1] 4\n", - "[86, 98, 96, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 50, 31, 1] 4\n", - "[86, 100, 62, 2] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 50, 41, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[43, 51, 49, 1] 4\n", - "[86, 102, 98, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 1, 34, 1] 56\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 2, 5, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 2, 51, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 3, 37, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 4, 48, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 5, 47, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 6, 26, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 9, 0, 1] 115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 10, 11, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 10, 15, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 12, 28, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 15, 12, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 16, 22, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 17, 1, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 17, 38, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 18, 6, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 20, 3, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 21, 16, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 22, 14, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 23, 6, 1] 0\n", - "[88, 46, 12, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 24, 17, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 24, 44, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 25, 21, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 25, 50, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 26, 39, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 27, 21, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 27, 37, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 29, 48, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 30, 32, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 30, 43, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 31, 40, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 31, 46, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 32, 4, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 32, 18, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 33, 9, 1] -4\n", - "[88, 66, 18, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 36, 9, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 36, 44, 1] 8\n", - "[88, 72, 88, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 37, 19, 1] 4\n", - "[88, 74, 38, 2] 0\n", - "[132, 111, 57, 3] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 38, 34, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 39, 10, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 40, 30, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 41, 40, 1] 8\n", - "[88, 82, 80, 2] 4\n", - "[132, 123, 120, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 42, 31, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 43, 4, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 43, 29, 1] 4\n", - "[88, 86, 58, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 44, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 44, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 47, 45, 1] 4\n", - "[88, 94, 90, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 48, 33, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 48, 36, 1] 4\n", - "[88, 96, 72, 2] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 50, 7, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[44, 50, 16, 1] -4\n", - "[88, 100, 32, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 0, 6, 1] -67\n", - "\n", - "**********\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 1, 6, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 4, 19, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 5, 24, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 5, 36, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 6, 22, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 8, 10, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 9, 23, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 9, 42, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 10, 41, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 10, 49, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 12, 30, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 14, 5, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 14, 51, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 15, 40, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 17, 4, 1] 4\n", - "[90, 34, 8, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 17, 18, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 18, 16, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 20, 34, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 21, 8, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 22, 2, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 23, 7, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 23, 16, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 24, 32, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 26, 14, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 28, 43, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 29, 19, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 30, 3, 1] -8\n", - "[90, 60, 6, 2] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 30, 27, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 32, 21, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 32, 37, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 34, 26, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 34, 33, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 35, 5, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 37, 13, 1] -4\n", - "[90, 74, 26, 2] 0\n", - "[135, 111, 39, 3] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 38, 48, 1] 8\n", - "[90, 76, 96, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 40, 20, 1] 0\n", - "[90, 80, 40, 2] 8\n", - "[135, 120, 60, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 41, 45, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 42, 7, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 43, 37, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 44, 18, 1] 0\n", - "[90, 88, 36, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 44, 23, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 45, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 45, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 46, 20, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 46, 35, 1] 8\n", - "[90, 92, 70, 2] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 47, 9, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 47, 44, 1] 4\n", - "[90, 94, 88, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 49, 45, 1] 4\n", - "[90, 98, 90, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 50, 8, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 50, 28, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[45, 51, 24, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 1, 7, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 2, 19, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 3, 46, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 4, 8, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 4, 28, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 5, 22, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 6, 17, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 7, 32, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 8, 3, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 8, 27, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 9, 5, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 9, 51, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 11, 13, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 14, 48, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 15, 13, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 16, 32, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 16, 43, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 17, 50, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 18, 28, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 19, 10, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 20, 6, 1] 4\n", - "[92, 40, 12, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 21, 30, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 22, 4, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 22, 29, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 23, 24, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 25, 40, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 26, 38, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 27, 40, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 27, 46, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 28, 25, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 28, 27, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 29, 8, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 31, 9, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 31, 44, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 32, 12, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 33, 2, 1] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 35, 6, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 36, 2, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 38, 7, 0] -111\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 38, 16, 1] 0\n", - "[92, 76, 32, 2] 0\n", - "[138, 114, 48, 3] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 39, 34, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 40, 0, 1] 83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 41, 9, 1] -8\n", - "[92, 82, 18, 2] 0\n", - "[138, 123, 27, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 42, 24, 1] 4\n", - "[92, 84, 48, 2] 8\n", - "[138, 126, 72, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 42, 36, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 44, 51, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 45, 42, 1] 8\n", - "[92, 90, 84, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 46, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 46, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 47, 14, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 49, 39, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[46, 50, 30, 1] 4\n", - "[92, 100, 60, 2] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 0, 26, 1] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 1, 26, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 1, 33, 1] 56\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 2, 24, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 3, 13, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 5, 17, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 5, 44, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 6, 14, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 7, 2, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 8, 11, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 8, 15, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 9, 6, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 10, 40, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 11, 30, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 12, 43, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 15, 30, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 16, 2, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 17, 48, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 18, 22, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 19, 25, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 20, 47, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 22, 51, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 23, 22, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 24, 4, 1] -4\n", - "[94, 48, 8, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 24, 18, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 25, 8, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 26, 42, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 27, 13, 1] 4\n", - "[94, 54, 26, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 28, 11, 1] 4\n", - "[94, 56, 22, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 28, 29, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ characters ] sigma value\n", - "[47, 30, 37, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 31, 20, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 31, 35, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 32, 19, 1] 8\n", - "[94, 64, 38, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 33, 23, 1] 8\n", - "[94, 66, 46, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 33, 42, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 34, 9, 1] -4\n", - "[94, 68, 18, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 35, 47, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 36, 18, 1] 4\n", - "[94, 72, 36, 2] -8\n", - "[141, 108, 54, 3] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 36, 23, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 38, 33, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 38, 36, 1] 8\n", - "[94, 76, 72, 2] -4\n", - "[141, 114, 108, 3] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 39, 31, 1] 8\n", - "[94, 78, 62, 2] 0\n", - "[141, 117, 93, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 39, 41, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 40, 3, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 41, 20, 1] 0\n", - "[94, 82, 40, 2] 4\n", - "[141, 123, 60, 3] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 43, 19, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 44, 6, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 45, 34, 1] 8\n", - "[94, 90, 68, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 47, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 47, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[47, 51, 17, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 0, 13, 1] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 1, 13, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 4, 9, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 4, 44, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 5, 20, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 8, 51, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 10, 28, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 11, 17, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 12, 2, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 13, 21, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 13, 50, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 14, 40, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 14, 46, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 16, 42, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 17, 47, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 18, 9, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 19, 18, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 19, 23, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 22, 31, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 23, 39, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 24, 34, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 25, 22, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 28, 5, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 28, 51, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 29, 17, 1] 8\n", - "[96, 58, 34, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 29, 44, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 30, 48, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 31, 10, 1] 0\n", - "[96, 62, 20, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 32, 33, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 32, 36, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 35, 40, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 36, 34, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 38, 45, 1] 8\n", - "[96, 76, 90, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 39, 12, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 40, 11, 1] -4\n", - "[96, 80, 22, 2] -8\n", - "[144, 120, 33, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 40, 29, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 41, 43, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 42, 39, 1] 8\n", - "[96, 84, 78, 2] 0\n", - "[144, 126, 117, 3] 8\n", - "[192, 168, 156, 4] -4\n", - "[240, 210, 195, 5] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 43, 24, 1] 4\n", - "[96, 86, 48, 2] 4\n", - "[144, 129, 72, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 43, 36, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 45, 37, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 46, 11, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 46, 15, 1] -4\n", - "[96, 92, 30, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 47, 3, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 47, 27, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 48, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 48, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 49, 32, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 49, 43, 1] 8\n", - "[96, 98, 86, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 50, 14, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 51, 20, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[48, 51, 35, 1] 8\n", - "[96, 102, 70, 2] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 0, 22, 1] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 1, 22, 0] -51\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 2, 30, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 3, 9, 1] 36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 5, 32, 1] 48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 6, 2, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 7, 11, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 7, 29, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 8, 41, 1] 44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 8, 49, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 9, 7, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 9, 16, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 10, 45, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 12, 3, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 13, 31, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 14, 24, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 15, 20, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 16, 11, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 16, 15, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 17, 19, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 20, 33, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 20, 36, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 21, 10, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 22, 12, 1] 8\n", - "[98, 44, 24, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 24, 21, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 24, 37, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 25, 39, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 26, 51, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 27, 39, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 28, 49, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 31, 38, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 32, 13, 1] 0\n", - "[98, 64, 26, 2] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 33, 50, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 35, 24, 1] 8\n", - "[98, 70, 48, 2] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 35, 36, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 36, 21, 1] 4\n", - "[98, 72, 42, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 36, 50, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 40, 34, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 41, 1, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 41, 38, 1] 8\n", - "[98, 82, 76, 2] -4\n", - "[147, 123, 114, 3] 8\n", - "[196, 164, 152, 4] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 43, 13, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 44, 16, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 45, 6, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 46, 5, 1] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 47, 18, 1] 0\n", - "[98, 94, 36, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 47, 23, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 48, 25, 1] 4\n", - "[98, 96, 50, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 49, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 49, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 50, 10, 1] -8\n", - "[98, 100, 20, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 51, 32, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[49, 51, 43, 1] 8\n", - "[98, 102, 86, 2] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 0, 30, 1] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 1, 30, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 2, 39, 0] -47\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 4, 20, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 4, 35, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 5, 10, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 6, 3, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 6, 27, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 8, 6, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 10, 22, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 11, 14, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 12, 23, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 12, 42, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 13, 48, 0] -67\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 14, 13, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 16, 34, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 17, 40, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 17, 46, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 18, 20, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 19, 5, 1] 4\n", - "[100, 38, 10, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 20, 8, 1] 8\n", - "[100, 40, 16, 2] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 20, 28, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 21, 1, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 21, 38, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 24, 31, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 24, 41, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 25, 17, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 25, 44, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 26, 37, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 27, 17, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 28, 6, 1] -4\n", - "[100, 56, 12, 2] -36\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 29, 14, 1] 4\n", - "[100, 58, 28, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 29, 35, 0] -83\n", - "\n", - "**********\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 30, 7, 1] -4\n", - "[100, 60, 14, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 31, 25, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 33, 49, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 34, 43, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 35, 8, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 36, 41, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 36, 49, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 37, 38, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 39, 19, 1] 4\n", - "[100, 78, 38, 2] -8\n", - "[150, 117, 57, 3] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 40, 50, 1] 8\n", - "[100, 80, 100, 2] -28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 44, 40, 1] 8\n", - "[100, 88, 80, 2] 0\n", - "[150, 132, 120, 3] 4\n", - "[200, 176, 160, 4] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 45, 12, 1] -8\n", - "[100, 90, 24, 2] 4\n", - "[150, 135, 36, 3] 8\n", - "[200, 180, 48, 4] -8\n", - "[250, 225, 60, 5] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 46, 21, 1] 0\n", - "[100, 92, 42, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 46, 50, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 47, 11, 0] -107\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 47, 15, 1] -4\n", - "[100, 94, 30, 2] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 49, 2, 0] -119\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 50, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[50, 50, 1, 1] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 1, 39, 1] 56\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 2, 9, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 2, 44, 1] 52\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 4, 14, 0] -63\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 5, 0, 1] 123\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 7, 34, 0] -55\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 8, 48, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 9, 40, 0] -59\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 9, 46, 1] 40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 12, 4, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 12, 18, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 13, 12, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 14, 45, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 15, 32, 1] 32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 16, 5, 1] 8\n", - "[102, 32, 10, 2] -32\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 17, 26, 1] 28\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 18, 14, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 18, 35, 0] -71\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 19, 51, 0] -75\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 20, 13, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 21, 2, 1] 0\n", - "[102, 42, 4, 2] -48\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 22, 47, 0] -79\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 23, 20, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 23, 35, 1] 24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 24, 6, 1] 0\n", - "[102, 48, 12, 2] -40\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 26, 41, 1] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 26, 49, 0] -83\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 28, 48, 1] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 30, 16, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 31, 3, 1] -8\n", - "[102, 62, 6, 2] -44\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 31, 27, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 32, 22, 1] 8\n", - "[102, 64, 44, 2] -24\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 33, 31, 1] 12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 33, 41, 0] -87\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 34, 10, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 35, 13, 0] -103\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 36, 31, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 37, 2, 0] -115\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 38, 39, 0] -91\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 40, 21, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 40, 37, 1] 8\n", - "[102, 80, 74, 2] -12\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 41, 25, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 41, 27, 1] 8\n", - "[102, 82, 54, 2] -8\n", - "[153, 123, 81, 3] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 42, 20, 1] 0\n", - "[102, 84, 40, 2] -4\n", - "[153, 126, 60, 3] 20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 43, 22, 0] -99\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 44, 46, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 46, 37, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 48, 42, 1] 8\n", - "[102, 96, 84, 2] 8\n", - "[153, 144, 126, 3] 0\n", - "[204, 192, 168, 4] 4\n", - "[255, 240, 210, 5] -16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 49, 25, 1] 4\n", - "[102, 98, 50, 2] 16\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 50, 38, 0] -95\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 51, 0, 0] -20\n", - "\n", - "**********\n", - "Knot sum:\n", - "T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "[ characters ] sigma value\n", - "[51, 51, 1, 1] -20\n" - ] - } - ], - "source": [ - "m.smallest_cable()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0, 11, 0, 83, 0, 17, 13, 103]\n", - "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83) # T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n", - "sigma is big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n", - "[0, 13, 0, 97, 0, 19, 17, 109]\n", - "T(2, 19; 2, 97) # -T(2, 13; 2, 97) # T(2, 97) # -T(2, 17; 2, 97) # T(2, 13; 2, 109) # -T(2, 109) # T(2, 17; 2, 109) # -T(2, 19; 2, 109)\n", - "sigma is not big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n", - "[0, 17, 0, 107, 0, 23, 19, 131]\n", - "T(2, 23; 2, 107) # -T(2, 17; 2, 107) # T(2, 107) # -T(2, 19; 2, 107) # T(2, 17; 2, 131) # -T(2, 131) # T(2, 19; 2, 131) # -T(2, 23; 2, 131)\n", - "sigma is big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n", - "[0, 19, 0, 139, 0, 29, 23, 163]\n", - "T(2, 29; 2, 139) # -T(2, 19; 2, 139) # T(2, 139) # -T(2, 23; 2, 139) # T(2, 19; 2, 163) # -T(2, 163) # T(2, 23; 2, 163) # -T(2, 29; 2, 163)\n", - "sigma is big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n", - "[0, 23, 0, 139, 0, 31, 29, 163]\n", - "T(2, 31; 2, 139) # -T(2, 23; 2, 139) # T(2, 139) # -T(2, 29; 2, 139) # T(2, 23; 2, 163) # -T(2, 163) # T(2, 29; 2, 163) # -T(2, 31; 2, 163)\n", - "sigma is not big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n", - "[0, 29, 0, 163, 0, 37, 31, 181]\n", - "T(2, 37; 2, 163) # -T(2, 29; 2, 163) # T(2, 163) # -T(2, 31; 2, 163) # T(2, 29; 2, 181) # -T(2, 181) # T(2, 31; 2, 181) # -T(2, 37; 2, 181)\n", - "sigma is big for all metabolizers\n", - "\n", - "\n", - "\n", - "\n" - ] - } - ], - "source": [ - "m.few_cable_without_calc()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "ename": "AttributeError", - "evalue": "'NoneType' object has no attribute 'schema_short1'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprint_sigma_for_cable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;32m~/signature_function/gaknot/main.py\u001b[0m in \u001b[0;36mprint_sigma_for_cable\u001b[0;34m(verbose, Schemas)\u001b[0m\n\u001b[1;32m 129\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mprint_sigma_for_cable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSchemas\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 130\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m \u001b[0mschema_short1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSchemas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mschema_short1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 132\u001b[0m \u001b[0mschema_short2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSchemas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mschema_short2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 133\u001b[0m \u001b[0mschema_short\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSchemas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mschema_short\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'schema_short1'" - ] - } - ], - "source": [ - "m.print_sigma_for_cable()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "SageMath 9.0", - "language": "sage", - "name": "sagemath" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.10" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/notebooks/tests.ipynb b/notebooks/tests.ipynb index 9459cde..a66e688 100644 --- a/notebooks/tests.ipynb +++ b/notebooks/tests.ipynb @@ -12,7 +12,9 @@ "# display full output, not only last result, except ended with semicolon\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = 'all';\n", - "from IPython.display import Image, SVG" + "from IPython.display import Image, SVG\n", + "import logging\n", + "logging.basicConfig(level=logging.INFO)" ] }, { @@ -28,6 +30,17 @@ "m = import_sage('main', package='gaknot', path=path.module_path)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "m.prove_lemma(verbose=True)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -43,17 +56,17 @@ }, "outputs": [], "source": [ - "knot_formula = \"[[k[0], k[1], k[3]],\" + \\\n", - " \" [-k[1], -k[3]],\" + \\\n", - " \" [k[2], k[3]],\" + \\\n", - " \" [-k[0], -k[2], -k[3]]]\"\n", - "# q_vector = (3, 5, 7, 13)\n", - "q_vector = (3, 5, 7, 11)\n", + "# knot_formula = \"[[k[0], k[1], k[3]],\" + \\\n", + "# \" [-k[1], -k[3]],\" + \\\n", + "# \" [k[2], k[3]],\" + \\\n", + "# \" [-k[0], -k[2], -k[3]]]\"\n", + "# # q_vector = (3, 5, 7, 13)\n", + "# q_vector = (3, 5, 7, 11)\n", "\n", - "template = cs.CableTemplate(knot_formula, q_vector=q_vector, verbose=True)\n", - "cable = template.cable\n", - "# cable.plot_all_summands()\n", - "cable.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)" + "# template = cs.CableTemplate(knot_formula, q_vector=q_vector, verbose=True)\n", + "# cable = template.cable\n", + "# # cable.plot_all_summands()\n", + "# cable.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)" ] }, { @@ -80,11 +93,27 @@ "\n", "\n", "\n", - "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", - "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", - "cable_template = cable_template_1 + cable_template_2" + "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", + "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", + "# cable_template = cable_template_1 + cable_template_2" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# cable_template.knot_formula" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "markdown", "metadata": {}, @@ -98,17 +127,17 @@ "metadata": {}, "outputs": [], "source": [ - "q_vector = (5, 13, 19, 41,\\\n", - " 7, 17, 23, 43)\n", - "cable_template.fill_q_vector(q_vector=q_vector)\n", - "cable = cable_template.cable\n", - "print(cable.knot_description)\n", + "# q_vector = (5, 13, 19, 41,\\\n", + "# 7, 17, 23, 43)\n", + "# cable_template.fill_q_vector(q_vector=q_vector)\n", + "# cable = cable_template.cable\n", + "# print(cable.knot_description)\n", "\n", - "q_vector_small = (3, 7, 13, 19,\\\n", - " 5, 11, 17, 23)\n", - "cable_template.fill_q_vector(q_vector=q_vector)\n", - "cable = cable_template.cable\n", - "print(cable.knot_description)" + "# q_vector_small = (3, 7, 13, 19,\\\n", + "# 5, 11, 17, 23)\n", + "# cable_template.fill_q_vector(q_vector=q_vector)\n", + "# cable = cable_template.cable\n", + "# print(cable.knot_description)" ] }, { @@ -136,14 +165,14 @@ "outputs": [], "source": [ "\n", - "cable_template.fill_q_vector()\n", - "# print(cable_template.q_vector)\n", - "# print(cable_template.knot_formula)\n", + "# cable_template.fill_q_vector()\n", + "# # print(cable_template.q_vector)\n", + "# # print(cable_template.knot_formula)\n", "\n", - "slice_canidate = cable_template.cable\n", - "print(slice_canidate.knot_description)\n", - "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", - "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", + "# slice_canidate = cable_template.cable\n", + "# print(slice_canidate.knot_description)\n", + "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n", + "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "\n", "\n", "# cable.is_signature_big_for_all_metabolizers()\n" @@ -190,22 +219,22 @@ "\n", "\n", "\n", - "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", - "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", - "cable_template = cable_template_1 + cable_template_2\n", + "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", + "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", + "# cable_template = cable_template_1 + cable_template_2\n", "\n", - "cable_template.fill_q_vector()\n", - "# print(cable_template.q_vector)\n", - "# print(cable_template.knot_formula)\n", + "# cable_template.fill_q_vector()\n", + "# # print(cable_template.q_vector)\n", + "# # print(cable_template.knot_formula)\n", "\n", - "slice_canidate = cable_template.cable\n", - "print(slice_canidate.knot_description)\n", - "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", - "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", + "# slice_canidate = cable_template.cable\n", + "# print(slice_canidate.knot_description)\n", + "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n", + "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "\n", "\n", - "slice_canidate.q_order\n", - "# slice_canidate.is_signature_big_for_all_metabolizers()" + "# slice_canidate.q_order\n", + "# # slice_canidate.is_signature_big_for_all_metabolizers()" ] }, { @@ -226,20 +255,20 @@ "\n", "\n", "\n", - "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", - "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", - "cable_template = cable_template_1 + cable_template_2\n", - "cable_template.fill_q_vector()\n", + "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", + "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", + "# cable_template = cable_template_1 + cable_template_2\n", + "# cable_template.fill_q_vector()\n", "\n", - "slice_canidate = cable_template.cable\n", - "print(slice_canidate.knot_description)\n", + "# slice_canidate = cable_template.cable\n", + "# print(slice_canidate.knot_description)\n", "\n", - "slice_canidate.q_order\n", - "# slice_canidate.is_signature_big_for_all_metabolizers()\n", - "sigma = slice_canidate.get_sigma_as_function_of_theta()\n", - "# sigma((0, 6, 6, 0, 0,0,0,0))\n", - "# 13450/83\n", - "sigma((9, 9, 9, 9, 0,0,0,0))" + "# slice_canidate.q_order\n", + "# # slice_canidate.is_signature_big_for_all_metabolizers()\n", + "# sigma = slice_canidate.get_sigma_as_function_of_theta()\n", + "# # sigma((0, 6, 6, 0, 0,0,0,0))\n", + "# # 13450/83\n", + "# sigma((9, 9, 9, 9, 0,0,0,0))" ] }, { @@ -275,18 +304,18 @@ "\n", "\n", "\n", - "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", - "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", - "cable_template = cable_template_1 + cable_template_2\n", + "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", + "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", + "# cable_template = cable_template_1 + cable_template_2\n", "\n", - "cable_template.fill_q_vector()\n", - "# print(cable_template.q_vector)\n", - "# print(cable_template.knot_formula)\n", + "# cable_template.fill_q_vector()\n", + "# # print(cable_template.q_vector)\n", + "# # print(cable_template.knot_formula)\n", "\n", - "slice_canidate = cable_template.cable\n", - "print(slice_canidate.knot_description)\n", - "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", - "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", + "# slice_canidate = cable_template.cable\n", + "# print(slice_canidate.knot_description)\n", + "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n", + "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "# slice_canidate.is_signature_big_for_all_metabolizers()" ] }, @@ -311,20 +340,20 @@ "\n", "\n", "\n", - "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", - "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", - "cable_template = cable_template_1 + cable_template_2\n", + "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", + "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", + "# cable_template = cable_template_1 + cable_template_2\n", "\n", - "cable_template.fill_q_vector()\n", - "# print(cable_template.q_vector)\n", - "# print(cable_template.knot_formula)\n", + "# cable_template.fill_q_vector()\n", + "# # print(cable_template.q_vector)\n", + "# # print(cable_template.knot_formula)\n", "\n", - "slice_canidate = cable_template.cable\n", - "print(slice_canidate.knot_description)\n", - "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", - "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", - "slice_canidate.q_order\n", - "# slice_canidate.is_signature_big_for_all_metabolizers()\n" + "# slice_canidate = cable_template.cable\n", + "# print(slice_canidate.knot_description)\n", + "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n", + "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n", + "# slice_canidate.q_order\n", + "# # slice_canidate.is_signature_big_for_all_metabolizers()\n" ] }, { @@ -333,8 +362,8 @@ "metadata": {}, "outputs": [], "source": [ - "sf = slice_canidate()\n", - "sf = sf[2]" + "# sf = slice_canidate()\n", + "# sf = sf[2]" ] }, { @@ -343,7 +372,7 @@ "metadata": {}, "outputs": [], "source": [ - "sf.plot()" + "# sf.plot()" ] }, { @@ -360,24 +389,62 @@ "formula_2 = \"[[ k[1], k[7]], \" + \\\n", " \"[ -k[7]], \" + \\\n", " \"[ k[6], k[7]], \" + \\\n", - " \"[ -k[5], -k[7]]]\"\n", - "\n", - "\n", - "\n", - "\n", - "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", - "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", - "cable_template = cable_template_1 + cable_template_2\n", - "\n", - "cable_template.fill_q_vector()\n", + " \"[ -k[5], -k[7]]]\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", + "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", + "# cable_template = cable_template_1 + cable_template_2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# cable_template.knot_formula" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# cable_template.fill_q_vector()\n", "# print(cable_template.q_vector)\n", - "# print(cable_template.knot_formula)\n", - "\n", - "slice_canidate = cable_template.cable\n", - "print(slice_canidate.knot_description)\n", - "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", - "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", - "slice_canidate.q_order" + "# print(cable_template.knot_formula)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# cable_template.fill_q_vector()\n", + "# print(cable_template.q_vector)\n", + "# print(cable_template.knot_formula)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# slice_canidate = cable_template.cable\n", + "# print(slice_canidate.knot_description)\n", + "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n", + "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n", + "# slice_canidate.q_order" ] }, { @@ -399,7 +466,7 @@ }, "outputs": [], "source": [ - "slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)" + "# slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)" ] }, { @@ -410,7 +477,7 @@ }, "outputs": [], "source": [ - "slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGNATURE)" + "# slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGNATURE)" ] }, { @@ -419,10 +486,10 @@ "metadata": {}, "outputs": [], "source": [ - "sigma = slice_canidate.get_sigma_as_function_of_theta()\n", - "sigma((0, 6, 6, 0, 0,0,0,0))\n", - "# 13450/83\n", - "sigma((9, 0, 0, 9, 0,0,0,0))" + "# sigma = slice_canidate.get_sigma_as_function_of_theta()\n", + "# sigma((0, 6, 6, 0, 0,0,0,0))\n", + "# # 13450/83\n", + "# sigma((9, 0, 0, 9, 0,0,0,0))" ] }, { @@ -431,8 +498,8 @@ "metadata": {}, "outputs": [], "source": [ - "_, _, sf = slice_canidate((1, 1, 0, 0, 0,0,0,0))\n", - "sf" + "# _, _, sf = slice_canidate((1, 1, 0, 0, 0,0,0,0))\n", + "# sf" ] }, { @@ -441,7 +508,7 @@ "metadata": {}, "outputs": [], "source": [ - "sg.SignaturePloter.plot(sf)" + "# sg.SignaturePloter.plot(sf)" ] }, { @@ -453,7 +520,7 @@ "outputs": [], "source": [ "\n", - "slice_canidate.plot_sum_for_theta_vector([0r,4r,0r,4r,0r,0r,0r,0r], save_to_dir=True)" + "# slice_canidate.plot_sum_for_theta_vector([0r,4r,0r,4r,0r,0r,0r,0r], save_to_dir=True)" ] }, { @@ -462,7 +529,7 @@ "metadata": {}, "outputs": [], "source": [ - "sf.plot()\n" + "# sf.plot()\n" ] }, { @@ -470,7 +537,9 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "# help(cs.CableTemplate.get_q_vector)" + ] }, { "cell_type": "code",