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fix import_sage usage (part2)

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maria 2021-07-15 20:30:45 +02:00
parent a9784f4948
commit ebfc944e4e
5 changed files with 107 additions and 269826 deletions
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2
gaknot/__init__.py
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@ -4,8 +4,6 @@ r"""
This package contains calculations of signature functions for knots (cable sums) 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) A knot (cable sum) is encoded as a list where each element (also a list)
corresponds to a cable knot, e.g. a list corresponds to a cable knot, e.g. a list
[[1, 3], [2], [-1, -2], [-3]] encodes [[1, 3], [2], [-1, -2], [-3]] encodes

44
gaknot/cable_signature.sage
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@ -7,11 +7,21 @@ import re
from typing import Iterable from typing import Iterable
from collections import Counter from collections import Counter
from sage.arith.functions import LCM_list from sage.arith.functions import LCM_list
import importlib # import importlib
from .utility import import_sage
from . import signature as sig # preparsing sage script and import as module
if __name__ == '__main__': # TBD - check is this is optimal
from utility import import_sage
package = None
path = ''
else: # called from package
from .utility import import_sage
package = os.path.join( __name__.split('.')[0])
path = '../'
sg = import_sage('signature', package=package, path=path)
SIGMA = 0 SIGMA = 0
@ -101,14 +111,14 @@ class CableSummand:
results.append((e * ksi, -1 * sgn(k_n))) results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n))) results.append((1 - e * ksi, 1 * sgn(k_n)))
return sig.SignatureFunction(values=results) return sg.SignatureFunction(values=results)
@classmethod @classmethod
def get_satellite_part(cls, *knot_as_k_values, theta=0): def get_satellite_part(cls, *knot_as_k_values, theta=0):
patt_k = knot_as_k_values[-1] patt_k = knot_as_k_values[-1]
ksi = 1/(2 * abs(patt_k) + 1) ksi = 1/(2 * abs(patt_k) + 1)
satellite_part = sig.SignatureFunction() satellite_part = sg.SignatureFunction()
# For each knot summand consider k values in reversed order, # For each knot summand consider k values in reversed order,
# ommit k value for pattern. # ommit k value for pattern.
for layer_num, k in enumerate(knot_as_k_values[:-1][::-1]): for layer_num, k in enumerate(knot_as_k_values[:-1][::-1]):
@ -141,7 +151,7 @@ class CableSummand:
for a in range(k)}) for a in range(k)})
counter.update(Counter({(2 * a + 1)/(2 * q): signum counter.update(Counter({(2 * a + 1)/(2 * q): signum
for a in range(k + 1, q)})) for a in range(k + 1, q)}))
return sig.SignatureFunction(counter=counter) return sg.SignatureFunction(counter=counter)
def get_summand_signature_as_theta_function(self): def get_summand_signature_as_theta_function(self):
# knot_as_k_values = self.knot_as_k_values # knot_as_k_values = self.knot_as_k_values
@ -189,7 +199,7 @@ class CableSummand:
if save_path is not None: if save_path is not None:
file_name = self.get_file_name_for_summand_plot(theta) file_name = self.get_file_name_for_summand_plot(theta)
save_path = os.path.join(save_path, file_name) save_path = os.path.join(save_path, file_name)
sig.SignaturePloter.plot_sum_of_two(pp, sp, title=title, sg.SignaturePloter.plot_sum_of_two(pp, sp, title=title,
save_path=save_path) save_path=save_path)
def plot_summand_sigma(self): def plot_summand_sigma(self):
@ -352,18 +362,18 @@ class CableSum:
# file_name = re.sub(r', ', '_', str(thetas)) # file_name = re.sub(r', ', '_', str(thetas))
# file_name = re.sub(r'[\[\]]', '', str(file_name)) # file_name = re.sub(r'[\[\]]', '', str(file_name))
# file_path = os.path.join(save_path, file_name) # file_path = os.path.join(save_path, file_name)
# sig.SignaturePloter.plot_sum_of_two(pp, sp, title=title, # sg.SignaturePloter.plot_sum_of_two(pp, sp, title=title,
# save_path=file_path) # save_path=file_path)
# #
# if save_path is not None: # if save_path is not None:
# file_path = os.path.join(save_path, "all_" + file_name) # file_path = os.path.join(save_path, "all_" + file_name)
# sf_list = [knot.signature_as_function_of_theta(thetas[i])[2] # sf_list = [knot.signature_as_function_of_theta(thetas[i])[2]
# for i, knot in enumerate(self.knot_summands)] # for i, knot in enumerate(self.knot_summands)]
# sig.SignaturePloter.plot_many(*sf_list, cols=2) # sg.SignaturePloter.plot_many(*sf_list, cols=2)
# pp, sp, sf = knot.signature_as_function_of_theta(thetas[i]) # pp, sp, sf = knot.signature_as_function_of_theta(thetas[i])
# (pp + sp) = sp.plot # (pp + sp) = sp.plot
# #
# sig.SignatureFunction.plot_sum_of_two(pp, sp, title=title, # sg.SignatureFunction.plot_sum_of_two(pp, sp, title=title,
# save_path=file_path) # save_path=file_path)
@ -443,8 +453,8 @@ class CableSum:
verbose = kwargs['verbose'] verbose = kwargs['verbose']
thetas = self.parse_thetas(*thetas) thetas = self.parse_thetas(*thetas)
satellite_part = sig.SignatureFunction() satellite_part = sg.SignatureFunction()
pattern_part = sig.SignatureFunction() pattern_part = sg.SignatureFunction()
# for each cable knot (summand) in cable sum apply theta # for each cable knot (summand) in cable sum apply theta
for th, knot in zip(thetas, self.knot_summands): for th, knot in zip(thetas, self.knot_summands):
@ -682,7 +692,7 @@ CableSum.get_signature_as_function_of_theta.__doc__ = \
k - parameters for a cable: parameters k_i (i=1,.., n-1) for satelit knots k - parameters for a cable: parameters k_i (i=1,.., n-1) for satelit knots
T(2, 2k_i + 1) and - the last one - k_n for a pattern knot T(2, 2k_n + 1). T(2, 2k_i + 1) and - the last one - k_n for a pattern knot T(2, 2k_n + 1).
Returns a function that will take theta vector as an argument and return Returns a function that will take theta vector as an argument and return
an object sig.SignatureFunction. an object sg.SignatureFunction.
To calculate signature function for a cable sum and a theta values vector, To calculate signature function for a cable sum and a theta values vector,
use as below. use as below.
@ -728,7 +738,7 @@ CableSum.get_signature_as_function_of_theta.__doc__ = \
get_summand_signture_function_docsting = \ get_summand_signture_function_docsting = \
""" """
This function returns sig.SignatureFunction for previously defined single This function returns sg.SignatureFunction for previously defined single
cable T_(2, q) and a theta given as an argument. cable T_(2, q) and a theta given as an argument.
The cable was defined by calling function The cable was defined by calling function
get_summand_signature_as_theta_function(*arg) get_summand_signature_as_theta_function(*arg)
@ -743,7 +753,7 @@ signature_as_function_of_theta_docstring = \
""" """
Arguments: Arguments:
Returns object of sig.SignatureFunction class for a previously defined Returns object of sg.SignatureFunction class for a previously defined
connected sum of len(arg) cables. connected sum of len(arg) cables.
Accept len(arg) arguments: for each cable one theta parameter. Accept len(arg) arguments: for each cable one theta parameter.
If call with no arguments, all theta parameters are set to be 0. If call with no arguments, all theta parameters are set to be 0.
@ -756,7 +766,7 @@ signature_as_function_of_theta_docstring = \
# T(2, q_n) is a pattern knot for a single cable from a cable sum # T(2, q_n) is a pattern knot for a single cable from a cable sum
# theta: twist/character for the cable (value form v vector) # theta: twist/character for the cable (value form v vector)
# Return: # Return:
# sig.SignatureFunction created for pattern signature function # sg.SignatureFunction created for pattern signature function
# for a given cable and theta/character # for a given cable and theta/character
# Based on: # Based on:
# Proposition 9.8. in Twisted Blanchfield Pairing # Proposition 9.8. in Twisted Blanchfield Pairing
@ -769,6 +779,6 @@ signature_as_function_of_theta_docstring = \
# n integers that encode a single cable, i.e. # n integers that encode a single cable, i.e.
# values of q_i for T(2,q_0; 2,q_1; ... 2, q_n) # values of q_i for T(2,q_0; 2,q_1; ... 2, q_n)
# Return: # Return:
# a function that returns sig.SignatureFunction for this single cable # a function that returns sg.SignatureFunction for this single cable
# and a theta given as an argument # and a theta given as an argument
# """ # """

3
gaknot/utility.py
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@ -38,9 +38,11 @@ def import_sage(module_name, package=None, path=''):
module_path = os.path.join(path, module_name) module_path = os.path.join(path, module_name)
if os.path.isfile(sage_path): if os.path.isfile(sage_path):
# print("\nPreparsing sage file " + sage_name + ".")
os.system('sage --preparse {}'.format(sage_path)); os.system('sage --preparse {}'.format(sage_path));
os.system('mv {} {}.py'.format(python_path, module_path)) os.system('mv {} {}.py'.format(python_path, module_path))
if package is not None: if package is not None:
module_name = package + "." + module_name module_name = package + "." + module_name
@ -48,6 +50,7 @@ def import_sage(module_name, package=None, path=''):
return importlib.reload(sys.modules[module_name]) return importlib.reload(sys.modules[module_name])
return importlib.import_module(module_name, package=package) return importlib.import_module(module_name, package=package)
def parse_sage(module_name): def parse_sage(module_name):
dir = os.path.dirname(__file__) dir = os.path.dirname(__file__)

269546
notebooks/main.ipynb
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notebooks/tests.ipynb
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