first tests for cable with 8 direct summand

This commit is contained in:
Maria Marchwicka 2020-10-14 17:21:17 +02:00
parent 4c8df7468e
commit 8ddb06fdb8
3 changed files with 457 additions and 127 deletions

View File

@ -3,6 +3,9 @@ import numpy as np
import itertools as it
from typing import Iterable
from collections import Counter
from sage.arith.functions import LCM_list
import warnings
import re
SIGNATURE = 0
SIGMA = 1
@ -38,42 +41,23 @@ class SignatureFunction(object):
items = self.cnt_signature_jumps.items()
counter = Counter({(1 + k) / 2 : v for k, v in items})
counter.update(Counter({k / 2 : v for k, v in items}))
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
new_data.append((jump_arg/2, jump))
new_data.append((1/2 + jump_arg/2, jump))
assert SignatureFunction(values=new_data) == SignatureFunction(counter=counter)
return SignatureFunction(values=new_data)
return SignatureFunction(counter=counter)
def square_root(self):
# to read values for t^(1/2)
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg < 1/2:
new_data.append((2 * jump_arg, jump))
counter = Counter()
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg < 1/2:
counter[2 * jump_arg] = jump
assert SignatureFunction(values=new_data) == SignatureFunction(counter=counter)
return SignatureFunction(values=new_data)
return SignatureFunction(counter=counter)
def minus_square_root(self):
# to read values for t^(1/2)
items = self.cnt_signature_jumps.items()
counter = Counter()
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg >= 1/2:
counter[mod_one(2 * jump_arg)] = jump
counter2 = Counter({mod_one(2 * k) : v for k, v in items if k >= 1/2 })
assert counter2 == counter
counter = Counter({mod_one(2 * k) : v for k, v in items if k >= 1/2})
return SignatureFunction(counter=counter)
def is_big(self):
def extremum(self):
max = 0
current = 0
items = sorted(self.cnt_signature_jumps.items())
@ -88,15 +72,8 @@ class SignatureFunction(object):
def __rshift__(self, shift):
# A shift of the signature functions corresponds to the rotation.
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
new_data.append((mod_one(jump_arg + shift), jump))
sf = SignatureFunction(values=new_data)
counter = Counter({mod_one(k + shift) : v \
for k, v in self.cnt_signature_jumps.items()})
assert SignatureFunction(counter=counter) == \
SignatureFunction(values=new_data)
return SignatureFunction(counter=counter)
def __lshift__(self, shift):
@ -112,18 +89,18 @@ class SignatureFunction(object):
counter.update(other.cnt_signature_jumps)
return SignatureFunction(counter=counter)
def __sub__(self, other):
counter = copy(self.cnt_signature_jumps)
counter.subtract(other.cnt_signature_jumps)
return SignatureFunction(counter=counter)
def __eq__(self, other):
self_cnt = Counter({k : v for k, v in self.cnt_signature_jumps.items()
if v != 0})
other_cnt = Counter({k : v for k, v in other.cnt_signature_jumps.items()
if v != 0})
return self.cnt_signature_jumps == other.cnt_signature_jumps
def __sub__(self, other):
counter = copy(self.cnt_signature_jumps)
counter.subtract(other.cnt_signature_jumps)
return SignatureFunction(counter=counter)
def __str__(self):
result = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
@ -145,15 +122,11 @@ class SignatureFunction(object):
def total_sign_jump(self):
# Total signature jump is the sum of all jumps.
result = sum([j[1] for j in self.to_list()])
assert result == sum(v for _, v in self.cnt_signature_jumps.items())
return sum([j[1] for j in self.to_list()])
def to_list(self):
# Return signature jumps formated as a list
assert sorted(self.cnt_signature_jumps.items(), key = lambda x: x[0]) == \
sorted(self.cnt_signature_jumps.items())
return sorted(self.cnt_signature_jumps.items(), key = lambda x: x[0])
return sorted(self.cnt_signature_jumps.items())
def step_function_data(self):
# Transform the signature jump data to a format understandable
@ -210,7 +183,6 @@ class TorusCable(object):
def __init__(self, knot_formula, k_vector=None, q_vector=None):
self._knot_formula = knot_formula
# q_i = 2 * k_i + 1
if k_vector is not None:
self.k_vector = k_vector
@ -220,7 +192,6 @@ class TorusCable(object):
msg = "Please give a list of k (k_vector) or q values (q_vector)."
raise ValueError(msg)
# TBD property function
self._sigma_function = None
self._signature_as_function_of_theta = None
@ -239,9 +210,13 @@ class TorusCable(object):
self.get_signature_as_function_of_theta()
return self._signature_as_function_of_theta
# KNOT ENCODING
@property
def knot_formula(self):
return self._knot_formula
# @knot_formula.setter
# def knot_formula(self, knot_formula):
# self._knot_formula = knot_formula
@property
def knot_description(self):
@ -251,14 +226,33 @@ class TorusCable(object):
def knot_sum(self):
return self._knot_sum
@knot_sum.setter
def knot_sum(self, val):
self._knot_sum = val
self._knot_description = self.get_knot_descrption(val)
self._number_of_summands = len(val)
def knot_sum(self, knot_sum):
self._knot_sum = knot_sum
self._knot_description = self.get_knot_descrption(knot_sum)
self._last_k_list = [abs(i[-1]) for i in knot_sum]
self._last_q_list = [2 * i + 1 for i in self._last_k_list]
if any(n not in Primes() for n in self._last_q_list):
msg = "Incorrect q-vector. This implementation assumes that" + \
" all last q values are prime numbers.\n" + \
str(self._last_q_list)
raise ValueError(msg)
self.q_order = LCM_list(self._last_q_list)
@property
def number_of_summands(self):
return self._number_of_summands
def last_k_list(self):
return self._last_k_list
@property
def last_q_list(self):
return self._last_q_list
@property
def q_order(self):
return self._q_order
@q_order.setter
def q_order(self, val):
self._q_order = val
@property
def k_vector(self):
@ -266,6 +260,11 @@ class TorusCable(object):
@k_vector.setter
def k_vector(self, k):
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 += "\nk_vector " + str(k) + " \nknot_formula " \
+ str(self.knot_formula)
raise IndexError(msg)
self.knot_sum = eval(self.knot_formula)
self._q_vector = [2 * k_val + 1 for k_val in k]
@ -277,60 +276,91 @@ class TorusCable(object):
self.k_vector = [(q - 1)/2 for q in new_q_vector]
def add_with_shift(self, other):
# print("*" * 100)
# print("BEFORE")
# print(self.knot_description)
# print(self.knot_sum)
# print("*" * 100)
# print("BEFORE k_vectors self, other")
# print(self.k_vector)
# print(other.k_vector)
shift = len(self.k_vector)
formula = re.sub(r'\d+', lambda x: str(int(x.group()) + shift),
other.knot_formula)
knot_formula = self.knot_formula[:-1] + ",\n" + formula[1:]
k_vector = self.k_vector + other.k_vector
cable = TorusCable(knot_formula, k_vector=k_vector)
s_signature_as_function_of_theta = self.signature_as_function_of_theta
o_signature_as_function_of_theta = other.signature_as_function_of_theta
shift = len(self.knot_sum)
shift = len(self.knot_sum)
def signature_as_function_of_theta(*thetas, **kwargs):
result = s_signature_as_function_of_theta(*thetas[shift:]) + \
o_signature_as_function_of_theta(*thetas[0:shift])
return result
cable._signature_as_function_of_theta = signature_as_function_of_theta
# print("*" * 100)
# print("AFTER")
# print(self.knot_description)
# print(self.knot_formula)
# print(self.knot_sum)
# print("*" * 100)
# print("AFTER k_vector, q_vector")
# print(self.k_vector)
# print(self.q_vector)
return cable
def __add__(self, other):
if self.k_vector != other.k_vector:
msg = "k_vectors are different. k-vector preserving addition is " +\
"impossible. The function add_with_shift was called instead"
warnings.warn(msg)
# print("*" * 100)
# print("BEFORE")
# print(self.knot_description)
# print(self.knot_sum)
# print("*" * 100)
# print("BEFORE k_vectors self, other")
knot_formula = self.knot_formula[:-1] + ",\n" + other.knot_formula[1:]
cable = TorusCable(knot_formula, k_vector=self.k_vector)
s_signature_as_function_of_theta = self.signature_as_function_of_theta
o_signature_as_function_of_theta = other.signature_as_function_of_theta
# print("FUNCTIONS ")
# print(s_signature_as_function_of_theta([1,1,1,2]))
# print(o_signature_as_function_of_theta([1,1,1,2]))
# print("FUNCTIONS 1111")
# print(s_signature_as_function_of_theta([1,1,1,1]))
# print(o_signature_as_function_of_theta([1,1,1,1]))
shift = len(self.knot_sum)
def signature_as_function_of_theta(*thetas, **kwargs):
result = s_signature_as_function_of_theta(*thetas[shift:]) + \
o_signature_as_function_of_theta(*thetas[0:shift])
return result
cable._signature_as_function_of_theta = signature_as_function_of_theta
# print("*" * 100)
# print("AFTER")
# print(self.knot_description)
# print(self.knot_formula)
# print(self.knot_sum)
# print("*" * 100)
# print("AFTER k_vector, q_vector")
# print(self.k_vector)
# print(self.q_vector)
return cable
def update(self, other):
# TBD knot_formula etc.
print("*" * 100)
print("BEFORE")
print(self.knot_description)
print(self.knot_formula)
print(self.knot_sum)
self._knot_formula = self.knot_formula[:-1] + ",\n" + \
other.knot_formula[1:]
self.knot_sum += other.knot_sum
# self.signature_as_function_of_theta = \
# self.get_signature_as_function_of_theta() + \
# other.get_signature_as_function_of_theta()
print("*" * 100)
print("AFTER")
print(self.knot_description)
print(self.knot_formula)
print(self.knot_sum)
def get_sigma_function(self):
k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
last_q = 2 * k_4 + 1
ksi = 1/last_q
sigma_q_1 = self.get_untwisted_signature_function(k_1)
sigma_q_2 = self.get_untwisted_signature_function(k_2)
sigma_q_3 = self.get_untwisted_signature_function(k_3)
def sigma_function(theta_vector, print_results=False):
# "untwisted" part (Levine-Tristram signatures)
a_1, a_2, a_3, a_4 = theta_vector
untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
sigma_q_2(ksi * a_2) +
sigma_q_3(ksi * a_3) -
sigma_q_3(ksi * a_4) +
sigma_q_1(ksi * a_1 * 2) -
sigma_q_1(ksi * a_4 * 2))
# "twisted" part
tp = [0, 0, 0, 0]
for i, a in enumerate(theta_vector):
if a:
tp[i] = -last_q + 2 * a - 2 * (a^2/last_q)
twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
# if print_results:
# self.print_results_LT(theta_vector, untwisted_part)
# self.print_results_LT(theta_vector, twisted_part)
sigma_v = untwisted_part + twisted_part
return sigma_v
return sigma_function
@staticmethod
def extract_max(string):
numbers = re.findall(r'\d+', string)
numbers = map(int, numbers)
return max(numbers)
@staticmethod
def get_blanchfield_for_pattern(k_n, theta):
@ -394,10 +424,10 @@ class TorusCable(object):
# return the signature function of the T_{2,2k+1} torus knot
k = abs(j)
q = 2 * k + 1
w = ([((2 * a + 1)/(2 * q), -1 * sgn(j)) for a in range(k)] +
values = ([((2 * a + 1)/(2 * q), -1 * sgn(j)) for a in range(k)] +
[((2 * a + 1)/(2 * q), 1 * sgn(j))
for a in range(k + 1, 2 * k + 1)])
return SignatureFunction(values=w)
return SignatureFunction(values=values)
@staticmethod
def get_knot_descrption(knot_sum):
@ -426,19 +456,21 @@ class TorusCable(object):
# call with no arguments
if len_t == 0:
return signature_as_function_of_theta(*(len_a * [0]))
if len_t != len_a:
if isinstance(thetas, Iterable) and len(thetas[0]) == len_a:
if isinstance(thetas, Iterable):
if len(thetas[0]) == len_a:
thetas = thetas[0]
else:
msg = "This function takes exactly " + str(len_a) + \
" arguments or no argument at all (" + str(len_t) + \
" given)."
raise TypeError(msg)
sf = SignatureFunction()
untwisted_part = SignatureFunction()
# for each cable knot in cable sum apply theta
# print(self.knot_sum)
for i, knot in enumerate(self.knot_sum):
try:
ssf = self.get_summand_signature_as_theta_function(*knot)
@ -451,15 +483,16 @@ class TorusCable(object):
print("ValueError: " + str(e.args[0]) +\
" Please change " + str(i + 1) + ". parameter.")
return None
a = thetas[0]
if all(i == a or i == self.q_vector[-1] - a for i in thetas):
print()
print("\n" + "*" * 100)
print(self.knot_description)
print("one vector " + str(thetas))
print("max sf " + str(sf.is_big()))
print()
# assert untwisted_part.is_zero_everywhere()
# a = thetas[0]
# # last_q = abs (2 * self.knot_sum[-1][-1]) + 1
# if all(i == thetas[0] for i in thetas):
# print()
# print("\n" + "*" * 100)
# print(self.knot_description)
# print("one vector " + str(thetas))
# print("max sf " + str(sf.extremum()))
# print()
# # assert untwisted_part.is_zero_everywhere()
if verbose:
print()
@ -478,6 +511,7 @@ class TorusCable(object):
def get_summand_signature_as_theta_function(self, *knot_as_k_values):
def get_summand_signture_function(theta):
# TBD: another formula (for t^2) description
# TBD if theata condition
k_n = knot_as_k_values[-1]
if theta > 2 * abs(k_n):
msg = "k for the pattern in the cable is " + str(k_n) + \
@ -491,6 +525,7 @@ class TorusCable(object):
# untwisted part
# for each knot summand consider k values in reversed order
# ommit last k = k_n value
ksi = 1/(2 * abs(k_n) + 1)
for i, k in enumerate(knot_as_k_values[:-1][::-1]):
power = 2^i
@ -576,6 +611,41 @@ class TorusCable(object):
bad_vectors.append(vector)
return good_vectors, bad_vectors
def is_metaboliser(self, theta):
i = 1
sum = 0
for idx, el in enumerate(theta):
to_add = i * el^2
# print("i * el^2 " + str(i * el^2))
to_add /= self.last_q_list[idx]
sum += to_add
# print("i * el^2 % q_4: " + str(to_add))
# print("sum ", sum)
i *= -1
# if sum is integer
# continue
# if all(a in [1, last_q - 1] for a in vector):
# pass
# else:
# continue
# print(theta, end=" ")
# print(sum)
if sum.is_integer():
print("#" * 100)
print(theta)
return True
return False
# if self.is_value_for_vector_class_big(vector, sigma_or_sign):
# good_vectors.append(vector)
# else:
# # print(vector)
# bad_vectors.append(vector)
# return good_vectors, bad_vectors
# searching for signature == 0
def eval_cable_for_null_signature(self, print_results=False, verbose=False):
# search for zero combinations
@ -600,8 +670,8 @@ class TorusCable(object):
# for all v = s * [a_1, a_2, a_3, a_4] for s in [1, last_q - 1]
def is_value_for_vector_class_big(self, theta_vector, sigma_or_sign):
[a_1, a_2, a_3, a_4] = theta_vector
q_4 = self.q_vector[-1]
k_4 = self.k_vector[-1]
k_4 = self.knot_sum[-1][-1]
q_4 = 2 * k_4 + 1
max_sigma = 0
@ -616,7 +686,7 @@ class TorusCable(object):
[a_1, a_2, a_3, a_4]]
if sigma_or_sign == SIGNATURE:
sf = f(shifted_theta)
sig_v = sf.is_big()
sig_v = sf.extremum()
else:
sig_v = f(shifted_theta)
print(sig_v, end=" ")
@ -641,8 +711,47 @@ class TorusCable(object):
return True
return False
##############################################################################
# sigma function
def get_sigma_function(self):
if len(self.k_vector) != 4:
msg = "This function is not implemented for k_vectors " +\
"with len other than 4."
raise IndexError(msg)
k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
last_q = 2 * k_4 + 1
ksi = 1/last_q
sigma_q_1 = self.get_untwisted_signature_function(k_1)
sigma_q_2 = self.get_untwisted_signature_function(k_2)
sigma_q_3 = self.get_untwisted_signature_function(k_3)
def sigma_function(theta_vector, print_results=False):
# "untwisted" part (Levine-Tristram signatures)
a_1, a_2, a_3, a_4 = theta_vector
untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
sigma_q_2(ksi * a_2) +
sigma_q_3(ksi * a_3) -
sigma_q_3(ksi * a_4) +
sigma_q_1(ksi * a_1 * 2) -
sigma_q_1(ksi * a_4 * 2))
# "twisted" part
tp = [0, 0, 0, 0]
for i, a in enumerate(theta_vector):
if a:
tp[i] = -last_q + 2 * a - 2 * (a^2/last_q)
twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
# if print_results:
# self.print_results_LT(theta_vector, untwisted_part)
# self.print_results_LT(theta_vector, twisted_part)
sigma_v = untwisted_part + twisted_part
return sigma_v
return sigma_function
def print_results_LT(self, theta_vector, untwisted_part):
knot_description = self.knot_description
k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]

221
main.sage Normal file
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@ -0,0 +1,221 @@
#!/usr/bin/python
attach("cable_signature.sage")
attach("my_signature.sage")
import numpy as np
def main():
global cable, cab_2, cab_1, joined_formula
# self.knot_formula = "[[k[0], k[1], k[3]], " + \
# "[-k[1], -k[3]], " + \
# "[k[2], k[3]], " + \
# "[-k[0], -k[2], -k[3]]]"
# knot_formula = config.knot_formula
# q_vector = (3, 5, 7, 13)
# cab_to_update = TorusCable(knot_formula=knot_formula, q_vector=q_vector)
# q_vector = (3, 5, 7, 11)
# cab_to_add = TorusCable(knot_formula=knot_formula, q_vector=q_vector)
# cab_shifted = cab_to_update.add_with_shift(cab_to_add)
q_vector = (5, 13, 19, 41,\
5, 17, 23, 43)
knot_formula = "[[k[0], k[5], k[3]], " + \
"[-k[1], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[0], -k[2], -k[3]]]"
cab_1 = TorusCable(knot_formula=knot_formula, q_vector=q_vector)
knot_formula = "[[k[4], k[1], k[7]], " + \
"[-k[5], -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[4], -k[6], -k[7]]]"
cab_2 = TorusCable(knot_formula=knot_formula, q_vector=q_vector)
cable = cab_1 + cab_2
joined_formula = cable.knot_formula
def check_all_thetas(cable):
upper_bounds = cable.last_k_list[:4]
# upper_bounds += [0, 0, 0, 0]
ranges_list = [range(1, i + 1) for i in upper_bounds]
ranges_list += [range(0, 1) for _ in range(4)]
print(ranges_list)
for theta in it.product(*ranges_list):
# pass
if cable.is_metaboliser(theta):
print("\n" * 10)
print("!" * 100)
for shift in range(1, cable.q_order):
shifted_theta = [(shift * th) % cable.last_q_list[i]
for i, th in enumerate(theta)]
shifted_theta = [min(th, cable.last_q_list[i] - th)
for i, th in enumerate(shifted_theta)]
print(shifted_theta)
sf = cable.signature_as_function_of_theta(*shifted_theta)
extremum = abs(sf.extremum())
print(extremum)
if extremum > 5 + np.count_nonzero(shifted_theta):
print("ok")
break
else:
print("hliphlip")
print("!" * 100)
print("\n" * 10)
return
def get_q_vector(q_vector_size, lowest_number=1):
q = [lowest_number] * q_vector_size
P = Primes()
next_number = P.next(lowest_number)
for i in range(q_vector_size):
q[i] = next_number
next_number = P.next(4 * next_number)
return q
next_number = P.next(lowest_number)
for i, q in enumerate(q_vector):
q[i] = next_number
next_number = P.next(lowest_number)
q = [P.unrank(i + config.start_shift) for i in c]
ratio = q[3] > 4 * q[2] and q[2] > 4 * q[1] and q[1] > 4 * q[0]
if not ratio:
# print("Ratio-condition does not hold")
continue
print("q = ", q)
# cable = TorusCable(knot_formula=knot_formula, q_vector=q)
# list_of_ranges = config.get_list_of_ranges(cable.q_order)
# if cable.eval_cable_for_large_values(list_of_ranges, SIGMA,
# verbose=verbose,
# print_results=print_results):
# good_knots.append(cable.knot_description)
# return good_knots
# cab_to_update.update(cab_to_add)
# cab_to_update.update(cab_to_add)
# cab_to_update.update(cab_to_add)
# cab_to_update.update(cab_to_add)
pass
#
# def get_blanchfield_for_pattern(k_n, theta):
# if theta == 0:
# sf = TorusCable.get_untwisted_signature_function(k_n)
# return sf.square_root() + sf.minus_square_root()
#
# results = []
# k = abs(k_n)
# ksi = 1/(2 * k + 1)
#
# # print("lambda_odd, i.e. (theta + e) % 2 != 0")
# for e in range(1, k + 1):
# if (theta + e) % 2 != 0:
# results.append((e * ksi, 1 * sgn(k_n)))
# results.append((1 - e * ksi, -1 * sgn(k_n)))
# # print("\nlambda_even")
# # print("\nnormal")
# results_odd = results
# results = []
# for e in range(1, theta):
# if (theta + e) % 2 == 0:
# results.append((e * ksi, 1 * sgn(k_n)))
# results.append((1 - e * ksi, -1 * sgn(k_n)))
# # print(results)
# results_even_small = results
# results = []
# # print("reversed")
# for e in range(theta + 1, k + 1):
# if (theta + e) % 2 == 0:
# results.append((e * ksi, -1 * sgn(k_n)))
# results.append((1 - e * ksi, 1 * sgn(k_n)))
# # print(results)
# results_even_big = results
#
# return results_odd, results_even_small, results_even_big
# # return SignatureFunction(values=results)
#
# def main():
# prim = 3
# P = Primes()
# for it in range(20):
# prim = P.next(prim)
# k_j = (prim - 1)/2
# print(60 * "*")
# print("k is " + str(k_j))
# print(60 * "*")
#
# for i in range(1, k_j + 1):
#
# a, j, m = get_blanchfield_for_pattern(k_j, i)
# sf_j = SignatureFunction(j)
# sf_a = SignatureFunction(a)
# sf_m = SignatureFunction(m)
# sf_jam = sf_j + sf_a + sf_m
# assert TorusCable.get_blanchfield_for_pattern(k_j, i) == sf_jam
# af, jf, mf = get_blanchfield_for_pattern(-k_j, prim - i)
# print(60 * "*")
# print("lists")
# print(af)
# print(jf)
# print(mf)
# j = SignatureFunction(jf)
# a = SignatureFunction(af)
# m = SignatureFunction(mf)
# minus_jam = j + a + m
# values = cmp_blanchfield_for_pattern(-k_j, prim - i)
# print("sum of lists - 3 lists added")
# print(sorted(jf + af + mf))
#
# print("sum of lists - all values from Blanchfield")
# print(sorted(values))
#
# assert values == af + jf + mf
# print("not equeles - sf from all values")
#
# print(SignatureFunction(values))
# print("not equeles - sum of sf")
# print("sf for each list sep")
# print("jf")
# print(jf)
# print("af")
# print(af)
# print("mf")
# print(mf)
# print("sum of abouve sfs")
# print(minus_jam)
# assert TorusCable.get_blanchfield_for_pattern(-k_j, prim - i) == \
# SignatureFunction(values)
# assert TorusCable.get_blanchfield_for_pattern(-k_j, prim - i) == \
# minus_jam
#
#
# # a, j, m = get_blanchfield_for_pattern(k_j, 2 * k_j + 1 - i)
# # j = SignatureFunction(j)
# # a = SignatureFunction(a)
# # m = SignatureFunction(m)
#
# print("*" * 100)
# print("i is " + str(i) + ", q is " + str(2 * k_j + 1), " q - i is " + str(2 * k_j + 1 - i))
# print("*" * 100)
#
# ajm = sf_j + sf_a + sf_m
# ajm_minus = a + j + m
# print("4 times")
# print(ajm + ajm + ajm_minus + ajm_minus)
# print("is big")
# print((ajm + ajm + ajm_minus + ajm_minus).is_big())
# print()

View File

@ -141,7 +141,7 @@ def search_for_large_sigma_value(knot_formula=None, limit=None,
print("Ratio-condition does not hold")
continue
cable = TorusCable(knot_formula=knot_formula, q_vector=q)
list_of_ranges = config.get_list_of_ranges(cable.q_vector[-1])
list_of_ranges = config.get_list_of_ranges(cable.q_order)
if cable.eval_cable_for_large_values(list_of_ranges, SIGMA,
verbose=verbose,
print_results=print_results):