signature_function/gaknot/__init__.py

#!/usr/bin/env python3

r"""
This package contains calculations of signature functions for knots (cable sums)


It 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 .

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.
"""

from .utility import import_sage
import os

#
# package = __name__.split('.')[0]
# path = os.path.dirname(__file__)
# import_sage('signature', package=package, path=path)
# import_sage('cable_signature', package=package, path=path)
# import_sage('main', package=package, path=path)