268 lines
8.9 KiB
Python
268 lines
8.9 KiB
Python
#!/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('.')[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 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[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 [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" * 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 [2, 3, 5, 7, 11, 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" * 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=(1, 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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