First commit via PyCharm, refactor.
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@ -1,2 +1,53 @@
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#!/usr/bin/env python3
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r"""
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This package contains calculations of signature functions for knots (cable sums)
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It can be run as a sage script from the terminal or used in interactive mode.
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A knot (cable sum) is encoded as a list where each element (also a list)
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corresponds to a cable knot, e.g. a list
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[[1, 3], [2], [-1, -2], [-3]] encodes
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T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7).
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To calculate the number of characters for which signature function vanish use
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the function .
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sage: eval_cable_for_null_signature([[1, 3], [2], [-1, -2], [-3]])
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T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)
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Zero cases: 1
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All cases: 1225
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Zero theta combinations:
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(0, 0, 0, 0)
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sage:
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The numbers given to the function eval_cable_for_null_signature are k-values
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for each component/cable in a direct sum.
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To calculate signature function for a knot and a theta value, use function
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get_signature_as_function_of_theta (see help/docstring for details).
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About notation:
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Cables that we work with follow a schema:
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T(2, q_1; 2, q_2; 2, q_4) # -T(2, q_2; 2, q_4) #
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# T(2, q_3; 2, q_4) # -T(2, q_1; 2, q_3; 2, q_4)
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In knot_formula each k[i] is related with some q_i value, where
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q_i = 2*k[i] + 1.
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So we can work in the following steps:
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1) choose a schema/formula by changing the value of knot_formula
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2) set each q_i all or choose range in which q_i should varry
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3) choose vector v / theata vector.
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"""
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from .utility import import_sage
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import os
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package = __name__.split('.')[0]
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path = os.path.dirname(__file__)
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import_sage('signature', package=package, path=path)
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# import_sage('cable_signature', package=package, path=path)
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# import_sage('main', package=package, path=path)
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@ -15,14 +15,13 @@ SIGMA = 0
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SIGNATURE = 1
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# #############################################################################
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# 9.11 (9.8)
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# 9.15 (9.9)
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PLOTS_DIR = "../plots"
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class CableSummand:
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class CableSummand:
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def __init__(self, knot_as_k_values, verbose=False):
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@ -135,9 +134,9 @@ class CableSummand:
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else:
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raise ValueError('k or q value must be given')
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counter = Counter({(2 * a + 1)/(2 * q) : -signum
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counter = Counter({(2 * a + 1)/(2 * q): -signum
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for a in range(k)})
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counter.update(Counter({(2 * a + 1)/(2 * q) : signum
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counter.update(Counter({(2 * a + 1)/(2 * q): signum
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for a in range(k + 1, q)}))
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return sig.SignatureFunction(counter=counter)
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@ -20,86 +20,88 @@ package = __name__.split('.')[0]
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path = os.path.dirname(__file__)
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class Config:
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def __init__(self):
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self.f_results = os.path.join(os.getcwd(), "results.out")
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# class Config:
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# def __init__(self):
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# self.f_results = os.path.join(os.getcwd(), "results.out")
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self.short_3_layers_a = "[[ k[5], k[3]], " + \
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"[ -k[1], -k[3]], " + \
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"[ k[3]], " + \
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"[ -k[4], -k[6], -k[3]]]"
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self.short_3_layers_b = "[[k[4], k[1], k[7]], " + \
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"[ -k[7]], " + \
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"[k[6], k[7]], " + \
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"[-k[5], -k[7]]]"
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self.schema_short1 = "[ [k[5], k[3]], " + \
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"[ -k[1], -k[3]], " + \
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"[ k[3]], " + \
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"[ -k[6], -k[3]]]"
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self.schema_short2 = "[[ k[1], k[7]], " + \
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"[ -k[7]], " + \
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"[ k[6], k[7]], " + \
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"[ -k[5], -k[7]]]"
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self.schema_short = "[[ k[5], k[3]], " + \
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"[ -k[1], -k[3]], " + \
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"[ k[3]], " + \
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"[ -k[6], -k[3]], " + \
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"[ k[1], k[7]], " + \
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"[ -k[7]], " + \
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"[ k[6], k[7]], " + \
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"[ -k[5], -k[7]]]"
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class Schemas:
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self.two_summands_schema = "[\
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[k[0], k[1], k[4]], [-k[1], -k[3]],\
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[k[2], k[3]], [-k[0], -k[2], -k[4]]\
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]"
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knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]],\
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[-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
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knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
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[-k[0], -k[1], -k[3]], [-k[2]]]"
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# knot_formula = "[[k[0], k[1], k[2]],\
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# [ k[3], k[4]],\
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# [-k[0], -k[3], -k[4]],\
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# [ -k[1], -k[2]]]"
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#
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# knot_formula = "[[k[0], k[1], k[2]],\
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# [ k[3]],\
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# [-k[0], -k[1], -k[3]],\
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# [ -k[2]]]"
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short_3_layers_a = "[[ k[5], k[3]], " + \
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"[ -k[1], -k[3]], " + \
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"[ k[3]], " + \
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"[ -k[4], -k[6], -k[3]]]"
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self.two_small_summands_schema = "[[k[3]], [-k[3]],\
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[k[3]], [-k[3]] ]"
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short_3_layers_b = "[[k[4], k[1], k[7]], " + \
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"[ -k[7]], " + \
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"[ k[6], k[7]], " + \
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"[ -k[5], -k[7]]]"
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self.four_summands_schema = "[[k[3], k[2], k[0]],\
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[-k[2], -k[0]],\
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[k[1], k[0]],\
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[-k[3], -k[1], -k[0]]]"
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self.four_summands_schema = "[[k[0], k[1], k[3]]," + \
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" [-k[1], -k[3]]," + \
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" [k[2], k[3]]," + \
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" [-k[0], -k[2], -k[3]]]"
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formula_1 = "[[k[0], k[5], k[3]], " + \
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"[-k[1], -k[3]], " + \
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"[k[2], k[3]], " + \
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"[-k[0], -k[2], -k[3]]]"
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formula_2 = "[[k[4], k[1], k[7]], " + \
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"[-k[5], -k[7]], " + \
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"[k[6], k[7]], " + \
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"[-k[4], -k[6], -k[7]]]"
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formula_1 = "[[k[0], k[5], k[3]], " + \
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"[-k[5], -k[3]], " + \
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"[k[2], k[3]], " + \
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"[-k[4], -k[2], -k[3]]]"
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formula_2 = "[[k[4], k[1], k[7]], " + \
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"[-k[1], -k[7]], " + \
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"[k[6], k[7]], " + \
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"[-k[0], -k[6], -k[7]]]"
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schema_short1 = "[ [k[5], k[3]], " + \
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"[ -k[1], -k[3]], " + \
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"[ k[3]], " + \
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"[ -k[6], -k[3]]]"
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schema_short2 = "[[ k[1], k[7]], " + \
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"[ -k[7]], " + \
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"[ k[6], k[7]], " + \
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"[ -k[5], -k[7]]]"
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schema_short = "[[ k[5], k[3]], " + \
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"[ -k[1], -k[3]], " + \
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"[ k[3]], " + \
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"[ -k[6], -k[3]], " + \
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"[ k[1], k[7]], " + \
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"[ -k[7]], " + \
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"[ k[6], k[7]], " + \
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"[ -k[5], -k[7]]]"
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# two_summands_schema = "[ [k[0], k[1], k[4]], [-k[1], -k[3]],\
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# [k[2], k[3]], [-k[0], -k[2], -k[4]] ]"
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# two_small_summands_schema = "[[k[3]], [-k[3]],\
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# [k[3]], [-k[3]] ]"
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#
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# four_summands_schema = "[[k[3], k[2], k[0]],\
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# [ -k[2], -k[0]],\
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# [ k[1], k[0]],\
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# [-k[3], -k[1], -k[0]]]"
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#
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four_summands_schema = "[[ k[0], k[1], k[3]]," + \
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"[ -k[1], -k[3]]," + \
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"[ k[2], k[3]]," + \
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"[ -k[0], -k[2], -k[3]]]"
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# formula_1 = "[[ k[0], k[5], k[3]], " + \
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# "[ -k[1], -k[3]], " + \
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# "[ k[2], k[3]], " + \
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# "[ -k[0], -k[2], -k[3]]]"
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#
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# formula_2 = "[[ k[4], k[1], k[7]], " + \
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# "[ -k[5], -k[7]], " + \
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# "[ k[6], k[7]], " + \
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# "[ -k[4], -k[6], -k[7]]]"
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#
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# formula_1 = "[[ k[0], k[5], k[3]], " + \
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# "[ -k[5], -k[3]], " + \
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# "[ k[2], k[3]], " + \
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# "[-k[4], -k[2], -k[3]]]"
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#
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# formula_2 = "[[ k[4], k[1], k[7]], " + \
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# "[ -k[1], -k[7]], " + \
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# "[ k[6], k[7]], " + \
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# "[-k[0], -k[6], -k[7]]]"
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def main(arg=None):
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@ -110,13 +112,13 @@ def main(arg=None):
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conf = Config()
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cable_loop_with_details(conf)
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def print_sigma_for_cable(verbose=True, conf=None):
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conf = conf or Config()
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.schema_short
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schema_four = conf.four_summands_schema
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def print_sigma_for_cable(verbose=True, Schemas=None):
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schema_short1 = Schemas.schema_short1
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schema_short2 = Schemas.schema_short2
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schema_short = Schemas.schema_short
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schema_four = Schemas.four_summands_schema
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cable_template = cs.CableTemplate(knot_formula=schema_short)
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cable_template.fill_q_vector()
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@ -141,12 +143,11 @@ def print_sigma_for_cable(verbose=True, conf=None):
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# cable2.plot_sigma_for_summands()
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def cable_loop_with_details(verbose=True, conf=None):
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conf = conf or Config()
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def cable_loop_with_details(verbose=True):
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# verbose = False
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.schema_short
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schema_short1 = Schemas.schema_short1
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schema_short2 = Schemas.schema_short2
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schema_short = Schemas.schema_short
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cable_template = cs.CableTemplate(knot_formula=schema_short)
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list_of_q_vectors = []
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@ -174,12 +175,12 @@ def cable_loop_with_details(verbose=True, conf=None):
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print("sigma is not big for all metabolizers")
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print("\n" * 3)
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def few_cable_without_calc(verbose=False, conf=None):
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conf = conf or Config()
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.schema_short
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def few_cable_without_calc(verbose=False):
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schema_short1 = Schemas.schema_short1
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schema_short2 = Schemas.schema_short2
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schema_short = Schemas.schema_short
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cable_template = cs.CableTemplate(knot_formula=schema_short)
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@ -205,12 +206,12 @@ def few_cable_without_calc(verbose=False, conf=None):
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print("sigma is not big for all metabolizers")
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print("\n" * 3)
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def smallest_cable(verbose=True, conf=None):
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conf = conf or Config()
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.schema_short
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def smallest_cable(verbose=True):
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schema_short1 = Schemas.schema_short1
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schema_short2 = Schemas.schema_short2
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schema_short = Schemas.schema_short
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cable_template = cs.CableTemplate(knot_formula=schema_short)
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@ -225,6 +226,7 @@ def smallest_cable(verbose=True, conf=None):
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cable1.is_function_big_for_all_metabolizers(invariant=sigma)
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cable2.is_function_big_for_all_metabolizers(invariant=sigma)
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def plot_many_untwisted_signature_functions(range_tuple=(1, 10)):
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P = Primes()
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for i in range(*range_tuple):
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@ -234,8 +236,6 @@ def plot_many_untwisted_signature_functions(range_tuple=(1, 10)):
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if __name__ == '__main__':
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global config
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config = Config()
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if '__file__' in globals():
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# skiped in interactive mode as __file__ is not defined
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main(sys.argv)
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@ -243,8 +243,7 @@ if __name__ == '__main__':
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pass
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# main()
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#
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#
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# formula_long = "[[k[0], k[5], k[3]], " + \
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# "[-k[5], -k[3]], " + \
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# "[k[2], k[3]], " + \
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