signature_function/main.sage

169 lines
5.3 KiB
Python

#!/usr/bin/env sage -python
# TBD: read about Factory Method, variable in docstring, sage documentation,
# print calc. to output file
# delete separation for twisted_part and untwisted_part
# decide about printing option
import os
import sys
import itertools as it
import re
import numpy as np
attach("signature.sage")
attach("cable_signature.sage")
# if not os.path.isfile('signature.py'):
# os.system('sage --preparse cable_signature.sage')
# os.system('mv cable_signature.sage.py cable_signature.py')
# from signature import SignatureFunction
class Config(object):
def __init__(self):
self.f_results = os.path.join(os.getcwd(), "results.out")
self.verbose = True
# self.verbose = False
# knot_formula is a schema for knots which signature function
# will be calculated
self.knot_formula = "[[k[0], k[1], k[3]], " + \
"[-k[1], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[0], -k[2], -k[3]]]"
# self.knot_formula = "[[k[0], k[1], k[4]], [-k[1], -k[3]], \
# [k[2], k[3]], [-k[0], -k[2], -k[4]]]"
#
# self.knot_formula = "[[k[3]], [-k[3]], \
# [k[3]], [-k[3]] ]"
#
# self.knot_formula = "[[k[3], k[2], k[0]], [-k[2], -k[0]], \
# [k[1], k[0]], [-k[3], -k[1], -k[0]]]"
#
# self.knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]], \
# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
# self.knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
# [-k[0], -k[1], -k[3]], [-k[2]]]"
def main(arg=None):
try:
limit = int(arg[1])
except (IndexError, TypeError):
limit = None
# global cable_template , cable_template_2, cable_template_1
knot_formula = "[[k[0], k[1], k[3]], " + \
"[-k[1], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[0], -k[2], -k[3]]]"
template = CableTemplate(knot_formula, q_vector=[3, 5, 7, 11])
cab = template.cable
# cab.plot_all_summands()
cab.plot_sum_for_theta_vector([0,4,0,4], save_to_dir=True)
# knot_formula = config.knot_formula
# q_vector = (3, 5, 7, 13)
# q_vector = (3, 5, 7, 11)
return
formula_1 = "[[k[0], k[5], k[3]], " + \
"[-k[1], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[0], -k[2], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[-k[5], -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[4], -k[6], -k[7]]]"
q_vector = (5, 13, 19, 41,\
7, 17, 23, 43)
q_vector_small = (3, 7, 13, 19,\
5, 11, 17, 23)
cable_template_1 = CableTemplate(knot_formula=formula_1)
cable_template_2 = CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
# cable_with_shift = cable_template_1.add_with_shift(cable_template_2)
print(cable_with_shift.knot_formula)
# cable_template.fill_q_vector()
# print(cable_template.q_vector)
# print(cable_template.knot_formula)
cable = cable_template.cable
sf = cable(4,4,4,4,0,0,0,0)
sf = cable_template.cable.signature_as_function_of_theta(4,1,1,4,0,0,0,0)
# cable_template.cable.is_signature_big_for_all_metabolizers()
cable_template_1 = CableTemplate(knot_formula=formula_1)
cable_template_2 = CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
# cable_template.cable.is_signature_big_for_all_metabolizers()
sf = cable_template.cable.signature_as_function_of_theta(4,4,4,4,0,0,0,0)
if __name__ == '__main__':
global config
config = Config()
if '__file__' in globals():
# skiped in interactive mode as __file__ is not defined
main(sys.argv)
else:
pass
# main()
"""
This script calculates signature functions for knots (cable sums).
The script can be run as a sage script from the terminal
or used in interactive mode.
A knot (cable sum) is encoded as a list where each element (also a list)
corresponds to a cable knot, e.g. a list
[[1, 3], [2], [-1, -2], [-3]] encodes
T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7).
To calculate the number of characters for which signature function vanish use
the function eval_cable_for_null_signature as shown below.
sage: eval_cable_for_null_signature([[1, 3], [2], [-1, -2], [-3]])
T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)
Zero cases: 1
All cases: 1225
Zero theta combinations:
(0, 0, 0, 0)
sage:
The numbers given to the function eval_cable_for_null_signature are k-values
for each component/cable in a direct sum.
To calculate signature function for a knot and a theta value, use function
get_signature_as_function_of_theta (see help/docstring for details).
About notation:
Cables that we work with follow a schema:
T(2, q_1; 2, q_2; 2, q_4) # -T(2, q_2; 2, q_4) #
# T(2, q_3; 2, q_4) # -T(2, q_1; 2, q_3; 2, q_4)
In knot_formula each k[i] is related with some q_i value, where
q_i = 2*k[i] + 1.
So we can work in the following steps:
1) choose a schema/formula by changing the value of knot_formula
2) set each q_i all or choose range in which q_i should varry
3) choose vector v / theata vector.
"""