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gaknot/main.py
278
gaknot/main.py
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# This file was *autogenerated* from the file /home/maria/signature_function/gaknot/main.sage
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from sage.all_cmdline import * # import sage library
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_sage_const_0 = Integer(0); _sage_const_1 = Integer(1); _sage_const_2 = Integer(2); _sage_const_3 = Integer(3); _sage_const_5 = Integer(5); _sage_const_7 = Integer(7); _sage_const_11 = Integer(11); _sage_const_13 = Integer(13); _sage_const_10 = Integer(10)#!/usr/bin/env sage -python
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# TBD: read about Factory Method, variable in docstring, sage documentation,
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# print calc. to output file
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# decide about printing option
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# make __main__?
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import os
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import sys
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import itertools as it
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import re
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import numpy as np
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import importlib
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from .utility import import_sage
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# from . import signature as sig
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# from . import cable_signature as cs
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package = __name__.split('.')[_sage_const_0 ]
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path = os.path.dirname(__file__)
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print(path)
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sg = import_sage('signature', package='gaknot', path=path)
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cs = import_sage('cable_signature', package='gaknot', path=path)
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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 Schemas:
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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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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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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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try:
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limit = int(arg[_sage_const_1 ])
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except (IndexError, TypeError):
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limit = 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, 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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q_v = cable_template.q_vector
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print(q_v)
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print(cable_template.cable.knot_description)
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cable1 = cs.CableTemplate(knot_formula=schema_short1,
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verbose=verbose,
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q_vector=q_v
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).cable
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cable2 = cs.CableTemplate(knot_formula=schema_short2,
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verbose=verbose,
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q_vector=q_v
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).cable
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cable = cs.CableTemplate(knot_formula=schema_short1,
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verbose=verbose,
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q_vector=q_v
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).cable
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cable.plot_sigma_for_summands()
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# cable1.plot_sigma_for_summands()
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# cable2.plot_sigma_for_summands()
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def cable_loop_with_details(verbose=True):
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# 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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list_of_q_vectors = []
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# for el in [2, 3, 5, 7, 11, 13]:
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for el in [_sage_const_2 ]:
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cable_template.fill_q_vector(lowest_number=el)
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q_v = cable_template.q_vector
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print(q_v)
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print(cable_template.cable.knot_description)
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cable1 = cs.CableTemplate(knot_formula=schema_short1,
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verbose=verbose,
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q_vector=q_v
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).cable
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cable2 = cs.CableTemplate(knot_formula=schema_short2,
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verbose=verbose,
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q_vector=q_v
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).cable
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# print("\n")
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# print(cable1.knot_description)
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is_1 = cable1.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)
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is_2 = cable2.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)
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if is_1 and is_2:
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print("sigma is big for all metabolizers")
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else:
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print("sigma is not big for all metabolizers")
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print("\n" * _sage_const_3 )
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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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list_of_q_vectors = []
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for el in [_sage_const_2 , _sage_const_3 , _sage_const_5 , _sage_const_7 , _sage_const_11 , _sage_const_13 ]:
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cable_template.fill_q_vector(lowest_number=el)
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q_v = cable_template.q_vector
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print(q_v)
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print(cable_template.cable.knot_description)
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cable1 = cs.CableTemplate(knot_formula=schema_short1,
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verbose=verbose,
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q_vector=q_v
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).cable
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cable2 = cs.CableTemplate(knot_formula=schema_short2,
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verbose=verbose,
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q_vector=q_v
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).cable
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is_1 = cable1.is_function_big_for_all_metabolizers(invariant=sigma)
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is_2 = cable2.is_function_big_for_all_metabolizers(invariant=sigma)
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if is_1 and is_2:
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print("sigma is big for all metabolizers")
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else:
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print("sigma is not big for all metabolizers")
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print("\n" * _sage_const_3 )
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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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q_v = cable_template.q_vector
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print(q_v)
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cable1 = cs.CableTemplate(knot_formula=schema_short1,
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verbose=verbose,
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q_vector=q_v).cable
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cable2 = cs.CableTemplate(knot_formula=schema_short2,
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verbose=verbose,
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q_vector=q_v).cable
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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=(_sage_const_1 , _sage_const_10 )):
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P = Primes()
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for i in range(*range_tuple):
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q = P.unrank(i)
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a = cs.CableSummand.get_untwisted_signature_function(q=q)
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a.plot()
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if __name__ == '__main__':
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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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else:
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pass
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# main()
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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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# "[-k[4], -k[2], -k[3]]" + \
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# "[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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#
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#
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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[3]], " + \
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# "[-k[4], -k[6], -k[3]]]"
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#
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# formula_2 = "[[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[0], -k[5], -k[7]]]"
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#
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#
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@ -1,385 +0,0 @@
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# This file was *autogenerated* from the file /home/maria/signature_function/gaknot/signature.sage
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from sage.all_cmdline import * # import sage library
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_sage_const_0 = Integer(0); _sage_const_1 = Integer(1); _sage_const_2 = Integer(2); _sage_const_36 = Integer(36); _sage_const_10 = Integer(10); _sage_const_5 = Integer(5); _sage_const_0p3 = RealNumber('0.3'); _sage_const_0p7 = RealNumber('0.7'); _sage_const_0p05 = RealNumber('0.05'); _sage_const_4 = Integer(4); _sage_const_3 = Integer(3)#!/usr/bin/env sage -python
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from collections import Counter
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import matplotlib.pyplot as plt
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import inspect
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from PIL import Image
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from pathlib import Path
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import warnings
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from .utility import mod_one
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# 9.11 (9.8)
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# 9.15 (9.9)
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import sys
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import os
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JUPYTER = 'ipykernel'
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IPy_TERMINAL = 'IPython'
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def get_ipython_info():
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if JUPYTER in sys.modules:
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return JUPYTER
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elif IPy_TERMINAL in sys.modules:
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return IPy_TERMINAL
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return False
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global ipython_info
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ipython_info = get_ipython_info()
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class SignatureFunction:
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def __init__(self, values=None, counter=None, plot_title=''):
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# counter of signature jumps
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if counter is None:
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counter = Counter()
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values = values or []
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for k, v in values:
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counter[k] += v
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counter = Counter({k : v for k, v in counter.items() if v != _sage_const_0 })
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if any(k >= _sage_const_1 for k in counter.keys()):
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msg = "Signature function is defined on the interval [0, 1)."
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raise ValueError(msg)
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counter[_sage_const_0 ] += _sage_const_0
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counter[_sage_const_1 ] += _sage_const_0
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self.jumps_counter = counter
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self.plot_title = plot_title
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def __rshift__(self, shift):
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# A shift of the signature functions corresponds to the rotation.
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counter = Counter({mod_one(k + shift) : v \
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for k, v in self.jumps_counter.items()})
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return SignatureFunction(counter=counter)
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def __lshift__(self, shift):
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return self.__rshift__(-shift)
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def __neg__(self):
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counter = Counter()
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counter.subtract(self.jumps_counter)
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return SignatureFunction(counter=counter)
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def __add__(self, other):
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counter = copy(self.jumps_counter)
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counter.update(other.jumps_counter)
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if self.plot_title and other.plot_title:
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title = self.plot_title + " + " + other.plot_title
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else:
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title = self.plot_title or other.plot_title
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|
||||||
return SignatureFunction(counter=counter, plot_title=title)
|
|
||||||
|
|
||||||
def __sub__(self, other):
|
|
||||||
counter = copy(self.jumps_counter)
|
|
||||||
counter.subtract(other.jumps_counter)
|
|
||||||
return SignatureFunction(counter=counter)
|
|
||||||
|
|
||||||
def __mul__(self, number):
|
|
||||||
# scalar multiplication
|
|
||||||
counter = Counter({k : number * v \
|
|
||||||
for k, v in self.jumps_counter.items()})
|
|
||||||
return SignatureFunction(counter=counter)
|
|
||||||
|
|
||||||
def __rmul__(self, number):
|
|
||||||
return(self.__mul__(number))
|
|
||||||
|
|
||||||
def __eq__(self, other):
|
|
||||||
return self.jumps_counter == other.jumps_counter
|
|
||||||
|
|
||||||
def __str__(self):
|
|
||||||
result = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
|
|
||||||
for jump_arg, jump in sorted(self.jumps_counter.items())])
|
|
||||||
return result
|
|
||||||
|
|
||||||
def __repr__(self):
|
|
||||||
result = ''.join([str(jump_arg) + ": " + str(jump) + ", "
|
|
||||||
for jump_arg, jump in sorted(self.jumps_counter.items())])
|
|
||||||
return result[:-_sage_const_2 ] + "."
|
|
||||||
|
|
||||||
def __call__(self, arg):
|
|
||||||
# return the value of the signature function at the point arg, i.e.
|
|
||||||
# sum of all signature jumps that occur before arg
|
|
||||||
items = self.jumps_counter.items()
|
|
||||||
result = [jump for jump_arg, jump in items if jump_arg < mod_one(arg)]
|
|
||||||
return _sage_const_2 * sum(result) + self.jumps_counter[arg]
|
|
||||||
|
|
||||||
def double_cover(self):
|
|
||||||
# to read values for t^2
|
|
||||||
items = self.jumps_counter.items()
|
|
||||||
counter = Counter({(_sage_const_1 + k) / _sage_const_2 : v for k, v in items})
|
|
||||||
counter.update(Counter({k / _sage_const_2 : v for k, v in items}))
|
|
||||||
return SignatureFunction(counter=counter)
|
|
||||||
|
|
||||||
def square_root(self):
|
|
||||||
# to read values for t^(1/2)
|
|
||||||
counter = Counter()
|
|
||||||
for jump_arg, jump in self.jumps_counter.items():
|
|
||||||
if jump_arg < _sage_const_1 /_sage_const_2 :
|
|
||||||
counter[_sage_const_2 * jump_arg] = jump
|
|
||||||
return SignatureFunction(counter=counter)
|
|
||||||
|
|
||||||
def minus_square_root(self):
|
|
||||||
# to read values for t^(1/2)
|
|
||||||
items = self.jumps_counter.items()
|
|
||||||
counter = Counter({mod_one(_sage_const_2 * k) : v for k, v in items if k >= _sage_const_1 /_sage_const_2 })
|
|
||||||
return SignatureFunction(counter=counter)
|
|
||||||
|
|
||||||
def is_zero_everywhere(self):
|
|
||||||
return not any(self.jumps_counter.values())
|
|
||||||
|
|
||||||
def extremum(self, limit=math.inf):
|
|
||||||
max_point = (_sage_const_0 , _sage_const_0 )
|
|
||||||
current = _sage_const_0
|
|
||||||
items = sorted(self.jumps_counter.items())
|
|
||||||
for arg, jump in items:
|
|
||||||
current += _sage_const_2 * jump
|
|
||||||
assert current == self(arg) + jump
|
|
||||||
if abs(current) > abs(max_point[_sage_const_1 ]):
|
|
||||||
max_point = (arg, current)
|
|
||||||
if abs(current) > limit:
|
|
||||||
break
|
|
||||||
return max_point
|
|
||||||
|
|
||||||
def total_sign_jump(self):
|
|
||||||
# Total signature jump is the sum of all jumps.
|
|
||||||
return sum([j[_sage_const_1 ] for j in sorted(self.jumps_counter.items())])
|
|
||||||
|
|
||||||
def plot(self, *args, **kargs):
|
|
||||||
SignaturePloter.plot(self, *args, **kargs)
|
|
||||||
|
|
||||||
|
|
||||||
class SignaturePloter:
|
|
||||||
|
|
||||||
@classmethod
|
|
||||||
def plot_many(cls, *sf_list, save_path=None, title='', cols=None):
|
|
||||||
|
|
||||||
axes_num = len(sf_list)
|
|
||||||
if axes_num > _sage_const_36 :
|
|
||||||
sf_list = sf_list[_sage_const_36 ]
|
|
||||||
axes_num = _sage_const_36
|
|
||||||
msg = "To many functions for the plot were given. "
|
|
||||||
msg += "Only 36 can be plotted "
|
|
||||||
warnings.warn(msg)
|
|
||||||
|
|
||||||
# print war, set val in conf
|
|
||||||
cols = cols or ceil(sqrt(axes_num))
|
|
||||||
rows = ceil(axes_num/cols)
|
|
||||||
fig, axes_matrix = plt.subplots(rows, cols,
|
|
||||||
sharex='col', sharey='row',
|
|
||||||
gridspec_kw={'hspace': _sage_const_0 , 'wspace': _sage_const_0 },
|
|
||||||
# sharey=True,
|
|
||||||
# sharex=True,
|
|
||||||
)
|
|
||||||
for i, sf in enumerate(sf_list):
|
|
||||||
col = i % cols
|
|
||||||
row = (i - col)/cols
|
|
||||||
sf.plot(subplot=True,
|
|
||||||
ax=axes_matrix[row][col],
|
|
||||||
title=sf.plot_title)
|
|
||||||
|
|
||||||
fig.suptitle(title)
|
|
||||||
plt.tight_layout()
|
|
||||||
|
|
||||||
cls.show_and_save(save_path)
|
|
||||||
|
|
||||||
@classmethod
|
|
||||||
def plot_sum_of_two(cls, sf1, sf2, save_path=None, title=''):
|
|
||||||
|
|
||||||
sf = sf1 + sf2
|
|
||||||
fig, axes_matrix = plt.subplots(_sage_const_2 , _sage_const_2 , sharey=True, figsize=(_sage_const_10 ,_sage_const_5 ))
|
|
||||||
|
|
||||||
sf1.plot(subplot=True,
|
|
||||||
ax=axes_matrix[_sage_const_0 ][_sage_const_1 ])
|
|
||||||
|
|
||||||
sf2.plot(subplot=True,
|
|
||||||
ax=axes_matrix[_sage_const_1 ][_sage_const_0 ],
|
|
||||||
color='red',
|
|
||||||
linestyle='dotted')
|
|
||||||
|
|
||||||
sf.plot(subplot=True,
|
|
||||||
ax=axes_matrix[_sage_const_0 ][_sage_const_0 ],
|
|
||||||
color='black')
|
|
||||||
|
|
||||||
sf1.plot(subplot=True,
|
|
||||||
ax=axes_matrix[_sage_const_1 ][_sage_const_1 ],
|
|
||||||
alpha=_sage_const_0p3 )
|
|
||||||
|
|
||||||
sf2.plot(subplot=True,
|
|
||||||
ax=axes_matrix[_sage_const_1 ][_sage_const_1 ],
|
|
||||||
color='red', alpha=_sage_const_0p3 ,
|
|
||||||
linestyle='dotted')
|
|
||||||
|
|
||||||
sf.plot(subplot=True,
|
|
||||||
ax=axes_matrix[_sage_const_1 ][_sage_const_1 ],
|
|
||||||
color='black',
|
|
||||||
alpha=_sage_const_0p7 ,)
|
|
||||||
|
|
||||||
fig.suptitle(title)
|
|
||||||
plt.tight_layout()
|
|
||||||
|
|
||||||
cls.show_and_save(save_path)
|
|
||||||
|
|
||||||
@classmethod
|
|
||||||
def plot(cls, sf, subplot=False, ax=None,
|
|
||||||
save_path=None,
|
|
||||||
title='',
|
|
||||||
alpha=_sage_const_1 ,
|
|
||||||
color='blue',
|
|
||||||
linestyle='solid',
|
|
||||||
special_point=None,
|
|
||||||
special_label='',
|
|
||||||
extraticks=None,
|
|
||||||
ylabel=''):
|
|
||||||
|
|
||||||
if ax is None:
|
|
||||||
fig, ax = plt.subplots(_sage_const_1 , _sage_const_1 )
|
|
||||||
|
|
||||||
keys = sorted(sf.jumps_counter.keys())
|
|
||||||
y = [(sf(k) + sf.jumps_counter[k]) for k in keys[:-_sage_const_1 ]]
|
|
||||||
xmax = keys[_sage_const_1 :]
|
|
||||||
xmin = keys[:-_sage_const_1 ]
|
|
||||||
|
|
||||||
ax.set(ylabel=ylabel)
|
|
||||||
ax.set(title=title)
|
|
||||||
ax.hlines(y, xmin, xmax, color=color, linestyle=linestyle, alpha=alpha)
|
|
||||||
if special_point is not None:
|
|
||||||
arg, val = special_point
|
|
||||||
extraticks = extraticks or []
|
|
||||||
plt.xticks(list(plt.xticks()[_sage_const_0 ]) + extraticks)
|
|
||||||
ext = sf.extremum()[_sage_const_1 ]
|
|
||||||
ytext = ext/_sage_const_2 + _sage_const_1 /_sage_const_2
|
|
||||||
xtext = arg + _sage_const_1 /_sage_const_5
|
|
||||||
|
|
||||||
ax.annotate(special_label, xy=(arg, val), xytext=(xtext, ytext),
|
|
||||||
arrowprops=dict(facecolor='black', shrink=_sage_const_0p05 ,
|
|
||||||
alpha=_sage_const_0p7 , width=_sage_const_2 ),)
|
|
||||||
if subplot:
|
|
||||||
return ax
|
|
||||||
|
|
||||||
cls.show_and_save(save_path)
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
def show_and_save(save_path):
|
|
||||||
|
|
||||||
if save_path is not None:
|
|
||||||
save_path = Path(save_path)
|
|
||||||
save_path = save_path.with_suffix('.png')
|
|
||||||
plt.savefig(save_path)
|
|
||||||
|
|
||||||
if ipython_info == JUPYTER:
|
|
||||||
plt.show()
|
|
||||||
|
|
||||||
elif True: # save_path is None:
|
|
||||||
plt.savefig('tmp.png')
|
|
||||||
plt.close()
|
|
||||||
image = Image.open('tmp.png')
|
|
||||||
image.show()
|
|
||||||
# msg = "For interactive shell set save_path."
|
|
||||||
# warnings.warn(msg)
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
def step_function_data(sf):
|
|
||||||
# Transform the signature jump data to a format understandable
|
|
||||||
# by the plot function.
|
|
||||||
result = [(k, sf.sf(k) + sf.jumps_counter[k])
|
|
||||||
for k in sorted(sf.jumps_counter.keys())]
|
|
||||||
return result
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
def tikz_plot(sf, save_as):
|
|
||||||
plt_sin = plot(sin(x), (x, _sage_const_0 , _sage_const_2 *pi))
|
|
||||||
# plt_sin.show()
|
|
||||||
plt_sin.save("MyPic.pdf")
|
|
||||||
|
|
||||||
return
|
|
||||||
# Draw the graph of the signature and transform it into TiKz.
|
|
||||||
# header of the LaTeX file
|
|
||||||
head = inspect.cleandoc(
|
|
||||||
r"""
|
|
||||||
\documentclass{standalone}
|
|
||||||
\usepackage{tikz}
|
|
||||||
\usetikzlibrary{calc}
|
|
||||||
\begin{document}
|
|
||||||
\begin{tikzpicture}
|
|
||||||
""")
|
|
||||||
|
|
||||||
body = \
|
|
||||||
r"""
|
|
||||||
%A piecewise linear function is drawn over the interval.
|
|
||||||
\draw (5,0) -- (6,-4);
|
|
||||||
%The axes are drawn.
|
|
||||||
\draw[latex-latex] ($(0,{-4*(2/5)}) +(0pt,-12.5pt)$) --
|
|
||||||
($(0,{4*(2/5)}) +(0pt,12.5pt)$) node[above right]{$y$};
|
|
||||||
\draw[latex-latex] ($({-4*(2/5)},0) +(-12.5pt,0pt)$) --
|
|
||||||
($({12*(2/5)},0) +(12.5pt,0pt)$) node[below right]{$x$};
|
|
||||||
"""
|
|
||||||
tail = \
|
|
||||||
r"""
|
|
||||||
\end{tikzpicture}
|
|
||||||
\end{document}
|
|
||||||
"""
|
|
||||||
tikzpicture = re.sub(r' +', ' ', ''.join([head, body, tail]))
|
|
||||||
tikzpicture = re.sub(r'\n ', '\n', tikzpicture)
|
|
||||||
|
|
||||||
with open("tmp.tex", "w") as f:
|
|
||||||
f.write(tikzpicture)
|
|
||||||
|
|
||||||
data = self.step_function_data()
|
|
||||||
with open(save_as, "w") as f:
|
|
||||||
head = \
|
|
||||||
r"""
|
|
||||||
\documentclass[tikz]{{standalone}}
|
|
||||||
%\usepackage{{tikz}}
|
|
||||||
\usetikzlibrary{{datavisualization}}
|
|
||||||
\usetikzlibrary{{datavisualization.formats.functions}}
|
|
||||||
%\usetikzlibrary{{calc}}
|
|
||||||
\begin{{document}}
|
|
||||||
\begin{{tikzpicture}}
|
|
||||||
\datavisualization[scientific axes, visualize as smooth line,
|
|
||||||
x axis={{ticks={{none,major={{at={{, {arg0} " as \\( {val0} \\
|
|
||||||
%]
|
|
||||||
""".format(arg0=str(N(data[_sage_const_0 ][_sage_const_0 ] ,digits=_sage_const_4 )), val0=str(data[_sage_const_0 ][_sage_const_0 ]))
|
|
||||||
f.write(head)
|
|
||||||
|
|
||||||
|
|
||||||
# f.write(", " + str(N(data[0][0],digits=4)) + " as \\(" + \
|
|
||||||
# str(data[0][0]) + "\\)")
|
|
||||||
for jump_arg, jump in data[_sage_const_1 :_sage_const_3 ]:
|
|
||||||
f.write(", " + str(N(jump_arg,digits=_sage_const_4 )) +
|
|
||||||
" as \\(" + str(jump_arg) + "\\)")
|
|
||||||
f.write("}}}}\n")
|
|
||||||
f.write(" ]\n")
|
|
||||||
f.write("data [format=function]{\n")
|
|
||||||
f.write("var x : interval [0:1];\n")
|
|
||||||
f.write("func y = \\value x;\n")
|
|
||||||
f.write("};\n")
|
|
||||||
# close LaTeX enviroments
|
|
||||||
tail = \
|
|
||||||
r"""
|
|
||||||
%};
|
|
||||||
\end{tikzpicture}
|
|
||||||
\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).
|
|
||||||
"""
|
|
||||||
|
|
||||||
Loading…
Reference in New Issue
Block a user