import sage defined only once in utility
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@ -8,24 +8,14 @@ from typing import Iterable
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from collections import Counter
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from collections import Counter
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from sage.arith.functions import LCM_list
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from sage.arith.functions import LCM_list
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import importlib
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import importlib
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from .utility import import_sage
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SIGMA = 0
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SIGMA = 0
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SIGNATURE = 1
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SIGNATURE = 1
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def import_sage(module_name):
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package = __name__.split('.')[0]
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path = os.path.dirname(__file__)
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sage_name = module_name + ".sage"
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sig = import_sage('signature', package=package, path=path)
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python_name = module_name + ".sage.py"
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if os.path.isfile(sage_name):
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os.system('sage --preparse {}'.format(sage_name));
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os.system('mv {} {}.py'.format(python_name, module_name))
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if module_name in sys.modules:
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return importlib.reload(sys.modules[module_name])
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return importlib.import_module(module_name, package=None)
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sig = import_sage('signature')
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# #############################################################################
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# #############################################################################
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@ -2,8 +2,8 @@
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# TBD: read about Factory Method, variable in docstring, sage documentation,
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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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# print calc. to output file
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# delete separation for twisted_part and untwisted_part
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# decide about printing option
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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 os
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import sys
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import sys
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@ -11,46 +11,93 @@ import sys
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import itertools as it
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import itertools as it
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import re
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import re
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import numpy as np
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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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attach("signature.sage")
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package = __name__.split('.')[0]
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attach("cable_signature.sage")
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path = os.path.dirname(__file__)
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sig = import_sage('signature', package=package, path=path)
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# if not os.path.isfile('signature.py'):
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cs = import_sage('cable_signature', package=package, path=path)
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# os.system('sage --preparse cable_signature.sage')
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# os.system('mv cable_signature.sage.py cable_signature.py')
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# from signature import SignatureFunction
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class Config:
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class Config(object):
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def __init__(self):
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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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self.f_results = os.path.join(os.getcwd(), "results.out")
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self.verbose = True
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self.short_3_layers_a = "[[ k[5], k[3]], " + \
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# self.verbose = False
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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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self.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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self.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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self.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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self.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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# knot_formula is a schema for knots which signature function
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self.two_summands_schema = "[\
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# will be calculated
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[k[0], k[1], k[4]], [-k[1], -k[3]],\
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self.knot_formula = "[[k[0], k[1], k[3]], " + \
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[k[2], k[3]], [-k[0], -k[2], -k[4]]\
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"[-k[1], -k[3]], " + \
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]"
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"[k[2], k[3]], " + \
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knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]],\
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"[-k[0], -k[2], -k[3]]]"
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[-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
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knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
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[-k[0], -k[1], -k[3]], [-k[2]]]"
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self.two_small_summands_schema = "[[k[3]], [-k[3]],\
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[k[3]], [-k[3]] ]"
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self.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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self.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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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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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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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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# self.knot_formula = "[[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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#
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# self.knot_formula = "[[k[3]], [-k[3]], \
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# [k[3]], [-k[3]] ]"
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#
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# self.knot_formula = "[[k[3], k[2], k[0]], [-k[2], -k[0]], \
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# [k[1], k[0]], [-k[3], -k[1], -k[0]]]"
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#
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# self.knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]], \
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# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
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# self.knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
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# [-k[0], -k[1], -k[3]], [-k[2]]]"
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@ -60,58 +107,130 @@ def main(arg=None):
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limit = int(arg[1])
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limit = int(arg[1])
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except (IndexError, TypeError):
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except (IndexError, TypeError):
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limit = None
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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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# global cable_template , cable_template_2, cable_template_1
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def print_sigma_for_cable(verbose=True, conf=None):
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knot_formula = "[[k[0], k[1], k[3]], " + \
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conf = conf or Config()
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"[-k[1], -k[3]], " + \
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schema_short1 = conf.schema_short1
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"[k[2], k[3]], " + \
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schema_short2 = conf.schema_short2
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"[-k[0], -k[2], -k[3]]]"
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schema_short = conf.schema_short
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template = CableTemplate(knot_formula, q_vector=[3, 5, 7, 11])
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schema_four = conf.four_summands_schema
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cab = template.cable
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# cab.plot_all_summands()
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cab.plot_sum_for_theta_vector([0,4,0,4], save_to_dir=True)
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# knot_formula = config.knot_formula
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# q_vector = (3, 5, 7, 13)
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# q_vector = (3, 5, 7, 11)
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return
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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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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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q_vector = (5, 13, 19, 41,\
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7, 17, 23, 43)
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q_vector_small = (3, 7, 13, 19,\
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5, 11, 17, 23)
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cable_template_1 = CableTemplate(knot_formula=formula_1)
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cable_template = cs.CableTemplate(knot_formula=schema_short)
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cable_template_2 = CableTemplate(knot_formula=formula_2)
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cable_template.fill_q_vector()
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cable_template = cable_template_1 + cable_template_2
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q_v = cable_template.q_vector
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# cable_with_shift = cable_template_1.add_with_shift(cable_template_2)
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print(q_v)
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print(cable_with_shift.knot_formula)
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print(cable_template.cable.knot_description)
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# cable_template.fill_q_vector()
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cable1 = cs.CableTemplate(knot_formula=schema_short1,
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# print(cable_template.q_vector)
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verbose=verbose,
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# print(cable_template.knot_formula)
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q_vector=q_v
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cable = cable_template.cable
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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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sf = cable(4,4,4,4,0,0,0,0)
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cable.plot_sigma_for_summands()
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# cable1.plot_sigma_for_summands()
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sf = cable_template.cable.signature_as_function_of_theta(4,1,1,4,0,0,0,0)
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# cable2.plot_sigma_for_summands()
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# cable_template.cable.is_signature_big_for_all_metabolizers()
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def cable_loop_with_details(verbose=True, conf=None):
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conf = conf or Config()
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# verbose = False
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.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, conf=None):
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conf = conf or Config()
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.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, conf=None):
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conf = conf or Config()
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schema_short1 = conf.schema_short1
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schema_short2 = conf.schema_short2
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schema_short = conf.schema_short
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cable_template_1 = CableTemplate(knot_formula=formula_1)
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cable_template = cs.CableTemplate(knot_formula=schema_short)
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cable_template_2 = CableTemplate(knot_formula=formula_2)
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q_v = cable_template.q_vector
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cable_template = cable_template_1 + cable_template_2
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print(q_v)
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# cable_template.cable.is_signature_big_for_all_metabolizers()
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cable1 = cs.CableTemplate(knot_formula=schema_short1,
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sf = cable_template.cable.signature_as_function_of_theta(4,4,4,4,0,0,0,0)
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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 __name__ == '__main__':
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@ -124,6 +243,29 @@ if __name__ == '__main__':
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pass
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pass
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# main()
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# main()
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#
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#
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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]], " + \
|
||||||
|
# "[-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).
|
||||||
|
|||||||
@ -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
|
||||||
|
|
||||||
@ -180,7 +193,7 @@ class SignaturePloter:
|
|||||||
fig, axes_matrix = plt.subplots(2, 2, sharey=True, figsize=(10,5))
|
fig, axes_matrix = plt.subplots(2, 2, sharey=True, figsize=(10,5))
|
||||||
|
|
||||||
sf1.plot(subplot=True,
|
sf1.plot(subplot=True,
|
||||||
ax=axes_matrix[0][1])
|
ax=axes_matrix[0][1])
|
||||||
|
|
||||||
sf2.plot(subplot=True,
|
sf2.plot(subplot=True,
|
||||||
ax=axes_matrix[1][0],
|
ax=axes_matrix[1][0],
|
||||||
@ -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
|
||||||
|
|
||||||
|
|||||||
@ -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))
|
||||||
Loading…
Reference in New Issue
Block a user