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import sage defined only once in utility

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This commit is contained in:
Maria Marchwicka 2021-01-11 07:34:03 +01:00
parent be469ccc2f
commit 4d2baf4e46
4 changed files with 296 additions and 92 deletions
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18
cagosig/cable_signature.sage
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@ -8,24 +8,14 @@ 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
SIGMA = 0 SIGMA = 0
SIGNATURE = 1 SIGNATURE = 1
def import_sage(module_name): package = __name__.split('.')[0]
path = os.path.dirname(__file__)
sage_name = module_name + ".sage" sig = import_sage('signature', package=package, path=path)
python_name = module_name + ".sage.py"
if os.path.isfile(sage_name):
os.system('sage --preparse {}'.format(sage_name));
os.system('mv {} {}.py'.format(python_name, module_name))
if module_name in sys.modules:
return importlib.reload(sys.modules[module_name])
return importlib.import_module(module_name, package=None)
sig = import_sage('signature')
# ############################################################################# # #############################################################################

284
cagosig/main.sage
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@ -2,8 +2,8 @@
# TBD: read about Factory Method, variable in docstring, sage documentation, # TBD: read about Factory Method, variable in docstring, sage documentation,
# print calc. to output file # print calc. to output file
# delete separation for twisted_part and untwisted_part
# decide about printing option # decide about printing option
# make __main__?
import os import os
import sys import sys
@ -11,46 +11,93 @@ import sys
import itertools as it import itertools as it
import re import re
import numpy as np import numpy as np
import importlib
from .utility import import_sage
attach("signature.sage") package = __name__.split('.')[0]
attach("cable_signature.sage") path = os.path.dirname(__file__)
sig = import_sage('signature', package=package, path=path)
# if not os.path.isfile('signature.py'): cs = import_sage('cable_signature', package=package, path=path)
# os.system('sage --preparse cable_signature.sage')
# os.system('mv cable_signature.sage.py cable_signature.py')
# from signature import SignatureFunction
class Config:
class Config(object):
def __init__(self): def __init__(self):
self.f_results = os.path.join(os.getcwd(), "results.out") self.f_results = os.path.join(os.getcwd(), "results.out")
self.verbose = True self.short_3_layers_a = "[[ k[5], k[3]], " + \
# self.verbose = False "[ -k[1], -k[3]], " + \
"[ k[3]], " + \
"[ -k[4], -k[6], -k[3]]]"
self.short_3_layers_b = "[[k[4], k[1], k[7]], " + \
"[ -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[5], -k[7]]]"
self.schema_short1 = "[ [k[5], k[3]], " + \
"[ -k[1], -k[3]], " + \
"[ k[3]], " + \
"[ -k[6], -k[3]]]"
self.schema_short2 = "[[ k[1], k[7]], " + \
"[ -k[7]], " + \
"[ k[6], k[7]], " + \
"[ -k[5], -k[7]]]"
self.schema_short = "[[ k[5], k[3]], " + \
"[ -k[1], -k[3]], " + \
"[ k[3]], " + \
"[ -k[6], -k[3]], " + \
"[ k[1], k[7]], " + \
"[ -k[7]], " + \
"[ k[6], k[7]], " + \
"[ -k[5], -k[7]]]"
# knot_formula is a schema for knots which signature function self.two_summands_schema = "[\
# will be calculated [k[0], k[1], k[4]], [-k[1], -k[3]],\
self.knot_formula = "[[k[0], k[1], k[3]], " + \ [k[2], k[3]], [-k[0], -k[2], -k[4]]\
]"
knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]],\
[-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
[-k[0], -k[1], -k[3]], [-k[2]]]"
self.two_small_summands_schema = "[[k[3]], [-k[3]],\
[k[3]], [-k[3]] ]"
self.four_summands_schema = "[[k[3], k[2], k[0]],\
[-k[2], -k[0]],\
[k[1], k[0]],\
[-k[3], -k[1], -k[0]]]"
self.four_summands_schema = "[[k[0], k[1], k[3]]," + \
" [-k[1], -k[3]]," + \ " [-k[1], -k[3]]," + \
" [k[2], k[3]]," + \ " [k[2], k[3]]," + \
" [-k[0], -k[2], -k[3]]]" " [-k[0], -k[2], -k[3]]]"
# self.knot_formula = "[[k[0], k[1], k[4]], [-k[1], -k[3]], \ formula_1 = "[[k[0], k[5], k[3]], " + \
# [k[2], k[3]], [-k[0], -k[2], -k[4]]]" "[-k[1], -k[3]], " + \
# "[k[2], k[3]], " + \
# self.knot_formula = "[[k[3]], [-k[3]], \ "[-k[0], -k[2], -k[3]]]"
# [k[3]], [-k[3]] ]" formula_2 = "[[k[4], k[1], k[7]], " + \
# "[-k[5], -k[7]], " + \
# self.knot_formula = "[[k[3], k[2], k[0]], [-k[2], -k[0]], \ "[k[6], k[7]], " + \
# [k[1], k[0]], [-k[3], -k[1], -k[0]]]" "[-k[4], -k[6], -k[7]]]"
#
# self.knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]], \ formula_1 = "[[k[0], k[5], k[3]], " + \
# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]" "[-k[5], -k[3]], " + \
# self.knot_formula = "[[k[0], k[1], k[2]], [k[3]],\ "[k[2], k[3]], " + \
# [-k[0], -k[1], -k[3]], [-k[2]]]" "[-k[4], -k[2], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[-k[1], -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[0], -k[6], -k[7]]]"
@ -60,58 +107,130 @@ def main(arg=None):
limit = int(arg[1]) limit = int(arg[1])
except (IndexError, TypeError): except (IndexError, TypeError):
limit = None limit = None
conf = Config()
cable_loop_with_details(conf)
# global cable_template , cable_template_2, cable_template_1 def print_sigma_for_cable(verbose=True, conf=None):
knot_formula = "[[k[0], k[1], k[3]], " + \ conf = conf or Config()
"[-k[1], -k[3]], " + \ schema_short1 = conf.schema_short1
"[k[2], k[3]], " + \ schema_short2 = conf.schema_short2
"[-k[0], -k[2], -k[3]]]" schema_short = conf.schema_short
template = CableTemplate(knot_formula, q_vector=[3, 5, 7, 11]) schema_four = conf.four_summands_schema
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 = cs.CableTemplate(knot_formula=schema_short)
cable_template_2 = CableTemplate(knot_formula=formula_2) cable_template.fill_q_vector()
cable_template = cable_template_1 + cable_template_2 q_v = cable_template.q_vector
# cable_with_shift = cable_template_1.add_with_shift(cable_template_2) print(q_v)
print(cable_with_shift.knot_formula) print(cable_template.cable.knot_description)
# cable_template.fill_q_vector() cable1 = cs.CableTemplate(knot_formula=schema_short1,
# print(cable_template.q_vector) verbose=verbose,
# print(cable_template.knot_formula) q_vector=q_v
cable = cable_template.cable ).cable
cable2 = cs.CableTemplate(knot_formula=schema_short2,
verbose=verbose,
q_vector=q_v
).cable
cable = cs.CableTemplate(knot_formula=schema_short1,
verbose=verbose,
q_vector=q_v
).cable
sf = cable(4,4,4,4,0,0,0,0) cable.plot_sigma_for_summands()
# cable1.plot_sigma_for_summands()
sf = cable_template.cable.signature_as_function_of_theta(4,1,1,4,0,0,0,0) # cable2.plot_sigma_for_summands()
# cable_template.cable.is_signature_big_for_all_metabolizers() def cable_loop_with_details(verbose=True, conf=None):
conf = conf or Config()
# verbose = False
schema_short1 = conf.schema_short1
schema_short2 = conf.schema_short2
schema_short = conf.schema_short
cable_template = cs.CableTemplate(knot_formula=schema_short)
list_of_q_vectors = []
# for el in [2, 3, 5, 7, 11, 13]:
for el in [2]:
cable_template.fill_q_vector(lowest_number=el)
q_v = cable_template.q_vector
print(q_v)
print(cable_template.cable.knot_description)
cable1 = cs.CableTemplate(knot_formula=schema_short1,
verbose=verbose,
q_vector=q_v
).cable
cable2 = cs.CableTemplate(knot_formula=schema_short2,
verbose=verbose,
q_vector=q_v
).cable
# print("\n")
# print(cable1.knot_description)
is_1 = cable1.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)
is_2 = cable2.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)
if is_1 and is_2:
print("sigma is big for all metabolizers")
else:
print("sigma is not big for all metabolizers")
print("\n" * 3)
def few_cable_without_calc(verbose=False, conf=None):
conf = conf or Config()
schema_short1 = conf.schema_short1
schema_short2 = conf.schema_short2
schema_short = conf.schema_short
cable_template = cs.CableTemplate(knot_formula=schema_short)
list_of_q_vectors = []
for el in [2, 3, 5, 7, 11, 13]:
cable_template.fill_q_vector(lowest_number=el)
q_v = cable_template.q_vector
print(q_v)
print(cable_template.cable.knot_description)
cable1 = cs.CableTemplate(knot_formula=schema_short1,
verbose=verbose,
q_vector=q_v
).cable
cable2 = cs.CableTemplate(knot_formula=schema_short2,
verbose=verbose,
q_vector=q_v
).cable
is_1 = cable1.is_function_big_for_all_metabolizers(invariant=sigma)
is_2 = cable2.is_function_big_for_all_metabolizers(invariant=sigma)
if is_1 and is_2:
print("sigma is big for all metabolizers")
else:
print("sigma is not big for all metabolizers")
print("\n" * 3)
def smallest_cable(verbose=True, conf=None):
conf = conf or Config()
schema_short1 = conf.schema_short1
schema_short2 = conf.schema_short2
schema_short = conf.schema_short
cable_template_1 = CableTemplate(knot_formula=formula_1) cable_template = cs.CableTemplate(knot_formula=schema_short)
cable_template_2 = CableTemplate(knot_formula=formula_2) q_v = cable_template.q_vector
cable_template = cable_template_1 + cable_template_2 print(q_v)
# cable_template.cable.is_signature_big_for_all_metabolizers() cable1 = cs.CableTemplate(knot_formula=schema_short1,
sf = cable_template.cable.signature_as_function_of_theta(4,4,4,4,0,0,0,0) verbose=verbose,
q_vector=q_v).cable
cable2 = cs.CableTemplate(knot_formula=schema_short2,
verbose=verbose,
q_vector=q_v).cable
cable1.is_function_big_for_all_metabolizers(invariant=sigma)
cable2.is_function_big_for_all_metabolizers(invariant=sigma)
def plot_many_untwisted_signature_functions(range_tuple=(1, 10)):
P = Primes()
for i in range(*range_tuple):
q = P.unrank(i)
a = cs.CableSummand.get_untwisted_signature_function(q=q)
a.plot()
if __name__ == '__main__': if __name__ == '__main__':
@ -124,6 +243,29 @@ if __name__ == '__main__':
pass pass
# main() # main()
#
#
# formula_long = "[[k[0], k[5], k[3]], " + \
# "[-k[5], -k[3]], " + \
# "[k[2], k[3]], " + \
# "[-k[4], -k[2], -k[3]]" + \
# "[k[4], k[1], k[7]], " + \
# "[-k[1], -k[7]], " + \
# "[k[6], k[7]], " + \
# "[-k[0], -k[6], -k[7]]]"
#
#
# formula_1 = "[[k[0], k[5], k[3]], " + \
# "[-k[1], -k[3]], " + \
# "[ k[3]], " + \
# "[-k[4], -k[6], -k[3]]]"
#
# formula_2 = "[[k[4], k[1], k[7]], " + \
# "[ -k[7]], " + \
# "[k[6], k[7]], " + \
# "[-k[0], -k[5], -k[7]]]"
#
#
""" """
This script calculates signature functions for knots (cable sums). This script calculates signature functions for knots (cable sums).

33
cagosig/signature.sage
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@ -9,6 +9,10 @@ import warnings
# 9.11 (9.8) # 9.11 (9.8)
# 9.15 (9.9) # 9.15 (9.9)
import sys
import os
JUPYTER = 'ipykernel' JUPYTER = 'ipykernel'
@ -74,6 +78,15 @@ class SignatureFunction:
counter.subtract(other.jumps_counter) counter.subtract(other.jumps_counter)
return SignatureFunction(counter=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): def __eq__(self, other):
return self.jumps_counter == other.jumps_counter return self.jumps_counter == other.jumps_counter
@ -211,25 +224,39 @@ class SignaturePloter:
cls.show_and_save(save_path) cls.show_and_save(save_path)
@classmethod @classmethod
def plot(cls, sf, subplot=False, ax=None, save_path=None, def plot(cls, sf, subplot=False, ax=None,
title="", save_path=None,
title='',
alpha=1, alpha=1,
color='blue', color='blue',
linestyle='solid', linestyle='solid',
special_point=None,
special_label='',
extraticks=None,
ylabel=''): ylabel=''):
if ax is None: if ax is None:
fig, ax = plt.subplots(1, 1) fig, ax = plt.subplots(1, 1)
keys = sorted(sf.jumps_counter.keys()) keys = sorted(sf.jumps_counter.keys())
y = [sf(k) + sf.jumps_counter[k] for k in keys] y = [(sf(k) + sf.jumps_counter[k]) for k in keys[:-1]]
xmax = keys[1:] xmax = keys[1:]
xmin = keys[:-1] xmin = keys[:-1]
ax.set(ylabel=ylabel) ax.set(ylabel=ylabel)
ax.set(title=title) ax.set(title=title)
ax.hlines(y, xmin, xmax, color=color, linestyle=linestyle, alpha=alpha) 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()[0]) + extraticks)
ext = sf.extremum()[1]
ytext = ext/2 + 1/2
xtext = arg + 1/5
ax.annotate(special_label, xy=(arg, val), xytext=(xtext, ytext),
arrowprops=dict(facecolor='black', shrink=0.05,
alpha=0.7, width=2),)
if subplot: if subplot:
return ax return ax

45
cagosig/utility.py
View File

@ -0,0 +1,45 @@
import importlib
import os
import sys
import re
def import_sage(module_name, package=None, path=None):
"""
Import or reload SageMath modules with preparse if the sage file exist.
"""
sage_name = module_name + ".sage"
python_name = module_name + ".sage.py"
if package is not None:
path_from_package_name = re.sub(r'\.', r'\\', package)
file_path = os.path.join('', path, path_from_package_name)
else:
file_path = os.path.join('', path)
sage_path = os.path.join(file_path, sage_name)
python_path = os.path.join(file_path, python_name)
module_path = os.path.join(file_path, module_name)
if os.path.isfile(sage_path):
os.system('sage --preparse {}'.format(sage_path));
os.system('mv {} {}.py'.format(python_path, module_path))
if package is not None:
module_name = package + "." + module_name
if module_name in sys.modules:
return importlib.reload(sys.modules[module_name])
return importlib.import_module(module_name, package=package)
def parse_sage(module_name):
dir = os.path.dirname(__file__)
sage_name = os.path.join(dir, module_name + ".sage")
python_name = os.path.join(dir, module_name + ".sage.py")
module_name = os.path.join(dir, module_name + ".py")
os.system('sage --preparse {}'.format(sage_name))
os.system('mv {} {}'.format(python_name, module_name))