refactoring
This commit is contained in:
Maria Marchwicka
parent
ac1a1d3475
commit
1824b075e9
@ -4,10 +4,13 @@ import numpy as np
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import itertools as it
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SIGNATURE = 0
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SIGMA = 1
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class TorusCable(object):
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def __init__(self, knot_formula, k_vector=None, q_vector=None):
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# q_i = 2 * k_i + 1
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if k_vector is None:
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if q_vector is None:
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# TBD docstring
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@ -27,8 +30,39 @@ class TorusCable(object):
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self.__sigma_function = None
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self.__signature_as_function_of_theta = None
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def __get_sigma_function(self):
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k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
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last_q = 2 * k_4 + 1
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ksi = 1/last_q
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sigma_q_1 = self.get_untwisted_signature_function(k_1)
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sigma_q_2 = self.get_untwisted_signature_function(k_2)
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sigma_q_3 = self.get_untwisted_signature_function(k_3)
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def get_untwisted_signature_function(self, j, q=None):
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def sigma_function(theta_vector, print_results=False):
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# "untwisted" part (Levine-Tristram signatures)
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a_1, a_2, a_3, a_4 = theta_vector
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untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
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sigma_q_2(ksi * a_2) +
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sigma_q_3(ksi * a_3) -
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sigma_q_3(ksi * a_4) +
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sigma_q_1(ksi * a_1 * 2) -
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sigma_q_1(ksi * a_4 * 2))
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# "twisted" part
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tp = [0, 0, 0, 0]
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for i, a in enumerate(theta_vector):
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if a:
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tp[i] = -last_q + 2 * a - 2 * (a^2/last_q)
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twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
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# if print_results:
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# self.print_results_LT(theta_vector, untwisted_part)
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# self.print_results_LT(theta_vector, twisted_part)
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sigma_v = untwisted_part + twisted_part
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return sigma_v
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return sigma_function
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@staticmethod
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def get_untwisted_signature_function(j, q=None):
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# return the signature function of the T_{2,2k+1} torus knot
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k = abs(j)
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q = 2 * k + 1
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@ -37,7 +71,6 @@ class TorusCable(object):
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for a in range(k + 1, 2 * k + 1)])
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return SignatureFunction(values=w)
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def get_knot_descrption(self):
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description = ""
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for knot in self.knot_sum:
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@ -116,30 +149,16 @@ class TorusCable(object):
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number_of_null_comb += 2^m
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return number_of_null_comb, list_of_good_vectors
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def eval_cable_for_large_signature(self, list_of_ranges,
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print_results=False,
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verbose=False):
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if self.__signature_as_function_of_theta is None:
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self.__signature_as_function_of_theta= \
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self.__get_signature_as_function_of_theta()
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if print_results:
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print()
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print(self.knot_description, end="\t\t\t")
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print()
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f = self.__signature_as_function_of_theta
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if self.s__check_all_combinations_in_ranges(list_of_ranges,
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print_results=print_results):
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return True
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return False
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def s__check_all_combinations_in_ranges(self, list_of_ranges,
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print_results=False):
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# searching for sigma > 5 + #(v_i != 0)
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def __check_all_combinations_in_ranges(self, list_of_ranges,
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sigma_or_sign,
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print_results=False):
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all_combinations_pass = True
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all_bad_vectors = []
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number_of_all_good_v = 0
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for i, range_product in enumerate(list_of_ranges):
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good_v, bad_v = self.s__check_combinations_in_range(range_product)
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good_v, bad_v = self.__check_combinations_in_range(range_product,
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sigma_or_sign)
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number_of_all_good_v += len(good_v)
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all_bad_vectors = list(it.chain(all_bad_vectors, bad_v))
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if bad_v:
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@ -157,53 +176,27 @@ class TorusCable(object):
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" : " + str(len(all_bad_vectors)))
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return all_combinations_pass
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def s__check_combinations_in_range(self, range_product):
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large_sigma_for_all_combinations = True
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# searching for signature or sigma > 5 + #(v_i != 0)
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def __check_combinations_in_range(self, range_product, sigma_or_sign):
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bad_vectors = []
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good_vectors = []
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q_4 = self.q_vector[-1]
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last_q = self.q_vector[-1]
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for vector in range_product:
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a_1, a_2, a_3, a_4 = vector
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if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
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if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % last_q:
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continue
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if all(a in [1, q_4 - 1] for a in vector):
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pass
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else:
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continue
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if self.s__is_sigma_for_vector_class_big(vector):
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# if all(a in [1, last_q - 1] for a in vector):
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# pass
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# else:
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# continue
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if self.__is_sigma_for_vector_class_big(vector, sigma_or_sign):
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good_vectors.append(vector)
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else:
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# print(vector)
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bad_vectors.append(vector)
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return good_vectors, bad_vectors
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def s__is_sigma_for_vector_class_big(self, theta_vector):
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[a_1, a_2, a_3, a_4] = theta_vector
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q_4 = self.q_vector[-1]
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k_4 = self.k_vector[-1]
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max_sigma = 0
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print(theta_vector, end="\t")
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for shift in range(1, k_4 + 1):
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shifted_theta = [(shift * a) % q_4 for a in
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[a_1, a_2, a_3, a_4]]
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sf = self.__signature_as_function_of_theta(shifted_theta)
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sigma_v = sf.is_big()
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print(sigma_v, end=" ")
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if abs(sigma_v) > abs(max_sigma):
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max_sigma = sigma_v
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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print("\tok " + str(sigma_v))
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return True
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print("\tbad class " + str(max_sigma))
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return False
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# searching for signature == 0
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def eval_cable_for_null_signature(self, print_results=False, verbose=False):
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# search for zero combinations
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@ -224,17 +217,35 @@ class TorusCable(object):
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return number_of_null_comb, number_of_all_comb
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return None
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# check sigma for all v = s * [a_1, a_2, a_3, a_4] for s in [1, q_4 - 1]
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def __is_sigma_for_vector_class_big(self, theta_vector):
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# check sigma for all v = s * [a_1, a_2, a_3, a_4] for s in [1, last_q - 1]
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def __is_sigma_for_vector_class_big(self, theta_vector, sigma_or_sign):
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[a_1, a_2, a_3, a_4] = theta_vector
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q_4 = self.q_vector[-1]
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k_4 = self.k_vector[-1]
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max_sigma = 0
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if sigma_or_sign == SIGNATURE:
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f = self.__signature_as_function_of_theta
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else:
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f = self.__sigma_function
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print(theta_vector, end="\t")
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for shift in range(1, k_4 + 1):
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shifted_theta = [(shift * a) % q_4 for a in
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[a_1, a_2, a_3, a_4]]
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sigma_v = self.__sigma_function(shifted_theta)
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if sigma_or_sign == SIGNATURE:
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sf = f(shifted_theta)
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sigma_v = sf.is_big()
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else:
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sigma_v = f(shifted_theta)
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print(sigma_v, end=" ")
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if abs(sigma_v) > abs(max_sigma):
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max_sigma = sigma_v
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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print("\tok " + str(sigma_v))
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return True
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print("\tbad class " + str(max_sigma))
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return False
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def __tmp_print_all_sigma_for_vector_class(self, theta_vector):
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@ -242,9 +253,9 @@ class TorusCable(object):
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print(self.knot_description)
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print("vector = " + str(theta_vector))
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[a_1, a_2, a_3, a_4] = theta_vector
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q_4 = self.q_vector[3]
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for shift in range(1, q_4):
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shifted_theta = [(shift * a) % q_4 for a in
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last_q = self.q_vector[-1]
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for shift in range(1, last_q):
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shifted_theta = [(shift * a) % last_q for a in
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[a_1, a_2, a_3, a_4]]
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print(str(shifted_theta) + "\t\t" + \
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str(self.__sigma_function(shifted_theta)))
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@ -253,9 +264,9 @@ class TorusCable(object):
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def __tmp_get_max_sigma_for_vector_class(self, theta_vector):
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max_sigma = (theta_vector, 0)
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[a_1, a_2, a_3, a_4] = theta_vector
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q_4 = self.q_vector[3]
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for shift in range(1, q_4):
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shifted_theta = [(shift * a) % q_4 for a in
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last_q = self.q_vector[-1]
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for shift in range(1, last_q):
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shifted_theta = [(shift * a) % last_q for a in
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[a_1, a_2, a_3, a_4]]
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sigma = self.__sigma_function(shifted_theta)
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if abs(sigma) > abs(max_sigma[1]):
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@ -265,45 +276,14 @@ class TorusCable(object):
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def is_sigma_for_vector_class_big(self, theta_vector):
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if self.__sigma_function is None:
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self.__sigma_function = self.__get_sigma_function()
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return self.__is_sigma_for_vector_class_big(theta_vector)
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def __get_sigma_function(self):
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k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
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q_4 = 2 * k_4 + 1
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ksi = 1/q_4
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sigma_q_1 = self.get_untwisted_signature_function(k_1)
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sigma_q_2 = self.get_untwisted_signature_function(k_2)
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sigma_q_3 = self.get_untwisted_signature_function(k_3)
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def sigma_function(theta_vector, print_results=False):
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# "untwisted" part (Levine-Tristram signatures)
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a_1, a_2, a_3, a_4 = theta_vector
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untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
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sigma_q_2(ksi * a_2) +
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sigma_q_3(ksi * a_3) -
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sigma_q_3(ksi * a_4) +
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sigma_q_1(ksi * a_1 * 2) -
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sigma_q_1(ksi * a_4 * 2))
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# "twisted" part
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tp = [0, 0, 0, 0]
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for i, a in enumerate(theta_vector):
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if a:
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tp[i] = -q_4 + 2 * a - 2 * (a^2/q_4)
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twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
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# if print_results:
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# self.print_results_LT(theta_vector, untwisted_part)
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# self.print_results_LT(theta_vector, twisted_part)
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sigma_v = untwisted_part + twisted_part
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return sigma_v
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return sigma_function
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return self.__is_sigma_for_vector_class_big(theta_vector, SIGMA)
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def print_results_LT(self, theta_vector, untwisted_part):
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knot_description = self.knot_description
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k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
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a_1, a_2, a_3, a_4 = theta_vector
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q_4 = 2 * k_4 + 1
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ksi = 1/q_4
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last_q = 2 * k_4 + 1
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ksi = 1/last_q
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sigma_q_1 = self.get_untwisted_signature_function(k_1)
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sigma_q_2 = self.get_untwisted_signature_function(k_2)
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sigma_q_3 = self.get_untwisted_signature_function(k_3)
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@ -378,7 +358,7 @@ class TorusCable(object):
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def print_results_sigma(self, theta_vector, twisted_part):
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a_1, a_2, a_3, a_4 = theta_vector
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knot_description = self.knot_description
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q_4 = self.q_vector[-1]
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last_q = self.q_vector[-1]
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print("\n\nSigma values for the cable sum: ")
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print(knot_description)
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print("and characters: " + str(v_theta))
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@ -388,29 +368,29 @@ class TorusCable(object):
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" = 0 if a == 0.")
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print("\nsigma(T_{2, q_4}, chi_a_1) = ", end="")
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if a_1:
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print("- (" + str(q_4) + ") + 2 * " + str(a_1) + " + " +\
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"- 2 * " + str(a_1^2) + "/" + str(q_4) + \
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print("- (" + str(last_q) + ") + 2 * " + str(a_1) + " + " +\
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"- 2 * " + str(a_1^2) + "/" + str(last_q) + \
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" = " + str(tp[0]))
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else:
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print("0")
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print("\nsigma(T_{2, q_4}, chi_a_2) = ", end ="")
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if a_2:
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print("- (" + str(q_4) + ") + 2 * " + str(a_2) + " + " +\
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"- 2 * " + str(a_2^2) + "/" + str(q_4) + \
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print("- (" + str(last_q) + ") + 2 * " + str(a_2) + " + " +\
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"- 2 * " + str(a_2^2) + "/" + str(last_q) + \
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" = " + str(tp[1]))
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else:
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print("0", end="")
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print("\nsigma(T_{2, q_4}, chi_a_3) = ", end="")
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if a_3:
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print("- (" + str(q_4) + ") + 2 * " + str(a_3) + " + " +\
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"- 2 * " + str(a_3^2) + "/" + str(q_4) + \
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print("- (" + str(last_q) + ") + 2 * " + str(a_3) + " + " +\
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"- 2 * " + str(a_3^2) + "/" + str(last_q) + \
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" = " + str(tp[2]))
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else:
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print("0", end="")
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print("\nsigma(T_{2, q_4}, chi_a_4) = ", end="")
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if a_4:
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print("- (" + str(q_4) + ") + 2 * " + str(a_4) + " + " +\
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"- 2 * " + str(a_4^2) + "/" + str(q_4) + \
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print("- (" + str(last_q) + ") + 2 * " + str(a_4) + " + " +\
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"- 2 * " + str(a_4^2) + "/" + str(last_q) + \
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" = " + str(tp[3]))
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else:
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print("0")
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@ -431,68 +411,34 @@ class TorusCable(object):
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self.__sigma_function = self.__get_sigma_function()
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return self.__sigma_function(theta_vector)
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# searching for sigma > 5 + #(v_i != 0)
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def __check_combinations_in_range(self, range_product):
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bad_vectors = []
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good_vectors = []
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q_4 = self.q_vector[-1]
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for vector in range_product:
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a_1, a_2, a_3, a_4 = vector
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if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
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continue
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# if all(a in [1, q_4 - 1] for a in vector):
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# continue
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if self.__is_sigma_for_vector_class_big(vector):
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good_vectors.append(vector)
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else:
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bad_vectors.append(vector)
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return good_vectors, bad_vectors
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# searching for sigma > 5 + #(v_i != 0)
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def check_combinations_in_range(self, range_product):
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if self.__sigma_function is None:
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self.__sigma_function = self.__get_sigma_function()
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return self.__check_combinations_in_range(range_product)
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return self.__check_combinations_in_range(range_product, SIGMA)
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# searching for sigma > 5 + #(v_i != 0)
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def __check_all_combinations_in_ranges(self, list_of_ranges,
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print_results=False):
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all_combinations_pass = True
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all_bad_vectors = []
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number_of_all_good_v = 0
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for i, range_product in enumerate(list_of_ranges):
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good_v, bad_v = self.__check_combinations_in_range(range_product)
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number_of_all_good_v += len(good_v)
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all_bad_vectors = list(it.chain(all_bad_vectors, bad_v))
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if bad_v:
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all_combinations_pass = False
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# if print_results:
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# print("good : bad:\t " + str(len(good_v)) +\
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# " : " + str(len(bad_v)))
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# if i in [0, 4,]:
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# print()
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# if bad_v:
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# print(bad_v)
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if print_results:
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print("good : bad:\t " + str(number_of_all_good_v) +\
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" : " + str(len(all_bad_vectors)))
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return all_combinations_pass
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# searching for sigma > 5 + #(v_i != 0)
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def eval_cable_for_large_sigma(self, list_of_ranges,
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print_results=False, verbose=False):
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if self.__sigma_function is None:
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self.__sigma_function = self.__get_sigma_function()
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def eval_cable_for_large_values(self, list_of_ranges,
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sigma_or_sign,
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print_results=False,
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verbose=False):
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if print_results:
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print(self.knot_description, end="\t\t\t")
|
||||
if sigma_or_sign == SIGMA:
|
||||
if self.__sigma_function is None:
|
||||
self.__sigma_function = self.__get_sigma_function()
|
||||
else:
|
||||
if self.__signature_as_function_of_theta is None:
|
||||
self.__signature_as_function_of_theta= \
|
||||
self.__get_signature_as_function_of_theta()
|
||||
|
||||
if self.__check_all_combinations_in_ranges(list_of_ranges,
|
||||
sigma_or_sign,
|
||||
print_results=print_results):
|
||||
return True
|
||||
return False
|
||||
|
||||
|
||||
|
||||
class SignatureFunction(object):
|
||||
|
||||
def __init__(self, values=None, counter=None):
|
||||
@ -586,7 +532,8 @@ class SignatureFunction(object):
|
||||
max = 0
|
||||
items = self.cnt_signature_jumps.items()
|
||||
for arg, _ in items:
|
||||
current = sum([jump for jump_arg, jump in items if jump_arg <= arg])
|
||||
# current = sum([jump for jump_arg, jump in items if jump_arg <= arg])
|
||||
current = self(arg)
|
||||
if abs(current) > abs(max):
|
||||
max = current
|
||||
if abs(max) > 9:
|
||||
@ -594,22 +541,10 @@ class SignatureFunction(object):
|
||||
return max
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
def mod_one(n):
|
||||
return n - floor(n)
|
||||
|
||||
|
||||
def get_untwisted_signature_function(j):
|
||||
# return the signature function of the T_{2,2k+1} torus knot
|
||||
k = abs(j)
|
||||
w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
|
||||
[((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
|
||||
for a in range(k + 1, 2 * k + 1)])
|
||||
return SignatureFunction(values=w)
|
||||
|
||||
|
||||
def get_summand_signature_as_theta_function(*arg):
|
||||
def get_summand_signture_function(theta):
|
||||
# TBD: another formula (for t^2) description
|
||||
@ -628,7 +563,7 @@ def get_summand_signature_as_theta_function(*arg):
|
||||
for i, k in enumerate(arg[:-1][::-1]):
|
||||
ksi = 1/(2 * k_n + 1)
|
||||
power = 2^i
|
||||
a = get_untwisted_signature_function(k)
|
||||
a = TorusCable.get_untwisted_signature_function(k)
|
||||
shift = theta * ksi * power
|
||||
b = a >> shift
|
||||
c = a << shift
|
||||
@ -709,15 +644,6 @@ def get_summand_signature_as_theta_function(*arg):
|
||||
return get_summand_signture_function
|
||||
|
||||
|
||||
def get_untwisted_signature_function(j):
|
||||
# return the signature function of the T_{2,2k+1} torus knot
|
||||
k = abs(j)
|
||||
w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
|
||||
[((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
|
||||
for a in range(k + 1, 2 * k + 1)])
|
||||
return SignatureFunction(values=w)
|
||||
|
||||
|
||||
TorusCable.get_number_of_combinations_of_theta.__doc__ = \
|
||||
"""
|
||||
Arguments:
|
||||
|
||||
@ -7,11 +7,11 @@ import sys
|
||||
|
||||
import itertools as it
|
||||
import re
|
||||
#
|
||||
|
||||
# if not os.path.isfile('cable_signature.py'):
|
||||
# os.system('sage --preparse cable_signature.sage')
|
||||
# os.system('mv cable_signature.sage.py cable_signature.py')
|
||||
# from cable_signature import SignatureFunction, TorusCable
|
||||
# from cable_signature import SignatureFunction, TorusCable, SIGNATURE, SIGMA
|
||||
|
||||
|
||||
class Config(object):
|
||||
@ -132,7 +132,8 @@ def search_for_large_sigma_value(knot_formula=None, limit=None,
|
||||
continue
|
||||
cable = TorusCable(knot_formula=knot_formula, q_vector=q)
|
||||
list_of_ranges = config.get_list_of_ranges(cable.k_vector[-1] + 1)
|
||||
if cable.eval_cable_for_large_sigma(list_of_ranges, verbose=verbose,
|
||||
if cable.eval_cable_for_large_values(list_of_ranges, SIGMA,
|
||||
verbose=verbose,
|
||||
print_results=print_results):
|
||||
good_knots.append(cable.knot_description)
|
||||
return good_knots
|
||||
@ -187,7 +188,8 @@ def search_for_large_signature_value(knot_formula=None, limit=None,
|
||||
continue
|
||||
cable = TorusCable(knot_formula=knot_formula, q_vector=q)
|
||||
list_of_ranges = config.get_list_of_ranges(cable.q_vector[-1])
|
||||
if cable.eval_cable_for_large_signature(list_of_ranges, verbose=verbose,
|
||||
if cable.eval_cable_for_large_values(list_of_ranges, SIGNATURE,
|
||||
verbose=verbose,
|
||||
print_results=print_results):
|
||||
good_knots.append(cable.knot_description)
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user