list of ranges, class Cable
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Maria Marchwicka
parent
4cdb4622ab
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1cc1de2e04
@ -216,22 +216,36 @@ class TorusCable(object):
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return None
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else:
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k_vector = [(q - 1)/2 for q in q_vector]
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# elif q_vector is None:
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# q_vector = [2 * k + 1 for k in k_vector]
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# self.knot_sum = eval(knot_formula)
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elif q_vector is None:
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q_vector = [2 * k + 1 for k in k_vector]
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self.knot_formula = knot_formula
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self.k_vector = k_vector
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self.q_vector = q_vector
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k = k_vector
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self.knot_sum = eval(knot_formula)
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self.knot_description = get_knot_descrption(*self.knot_sum)
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self.sigma_function = 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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[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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[a_1, a_2, a_3, a_4]]
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sigma_v = self.__calculate_sigma(shifted_theta)
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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return True
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return False
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def is_sigma_for_vector_class_big(self, theta_vector):
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return True
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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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print("settinf the function ")
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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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@ -267,180 +281,98 @@ class TorusCable(object):
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def __calculate_sigma(self, theta_vector):
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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_list):
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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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large_sigma_for_all_combinations = True
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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_list:
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a_1, a_2, a_3, a_4 = vector
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if a_1 == a_2 == a_3 == a_4:
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continue
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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 self.__is_sigma_for_vector_class_big(vector):
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good_vectors.append(vector)
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pass
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else:
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bad_vectors.append(vector)
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large_sigma_for_all_combinations = False
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return good_vectors, bad_vectors
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# def is_condition_for_vector_class_fulfilled(vector):
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# a_1, a_2, a_3, a_4 = vector
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# q_4 = self.q_vector[-1]
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# # check assumption - for results != 0 mod q_4 we stop here
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# if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
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# return None
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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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# searching for sigma > 5 + #(v_i != 0)
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def eval_cable_for_large_sigma(k_vector=None, knot_formula=None,
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print_results=True, verbose=None,
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q_vector=None):
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cable = TorusCable(knot_formula=knot_formula, k_vector=k_vector,
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q_vector=q_vector)
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# k is a k_vector
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k = cable.k_vector
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knot_description = cable.knot_description
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print("\n" * 5)
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print(knot_description)
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k_1, k_2, k_3, k_4 = [abs(i) for i in k]
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q_4 = 2 * k_4 + 1
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ksi = 1/q_4
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q = cable.q_vector[-1]
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if verbose:
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print("\n\n")
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print(100 * "*")
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print("Searching for a large signature values for the cable sum: ")
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print(knot_description)
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print(cable.knot_description)
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large_sigma_for_all_v_combinations = True
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bad_vectors = []
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good_vectors = []
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list_of_ranges = [
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# all characters a_1, a_2, a_3, a_4 != 0
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it.product(range(1, q), range(1, q), range(1, q), range(1, 2)),
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# iteration over all possible character combinations
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# T(2, q_1; 2, q_2; 2, q_4) # -T(2, q_2; 2, q_4) #
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# # T(2, q_3; 2, q_4) # -T(2, q_1; 2, q_3; 2, q_4)
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last_theta = 1
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large_sigma_for_last_theta_non_zero = True
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for vector in it.product(range(q_4), range(q_4), range(q_4)):
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v_theta = list(vector)
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v_theta.append(last_theta)
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# a_1 == 0, a_2, a_3, a_4 != 0
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it.product(range(1), range(1, q), range(1, q), range(1, 2)),
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# a_2 == 0, a_1, a_3, a_4 != 0
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it.product(range(1, q), range(1), range(1, q), range(1, 2)),
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# a_3 == 0, a_1, a_2, a_4 != 0
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it.product(range(1, q), range(1, q), range(1), range(1, 2)),
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# a_4 == 0, a_1, a_2, a_3 != 0
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it.product(range(1, q), range(1, q), range(1, 2), range(1)),
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a_1, a_2, a_3 = list(vector)
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a_4 = last_theta
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assert [a_1, a_2, a_3, a_4] == v_theta
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if a_1 == a_2 == a_3:
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if a_3 == 0:
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print("\na_1 == a_2 == a_3 == 0")
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continue
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elif a_3 == a_4:
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print("\nall a_i == a != 0")
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continue
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# a_1 == 0, a_2 == 0, a_3, a_4 != 0
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it.product(range(1), range(1), range(1, q), range(1, 2)),
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# a_1 == 0, a_3 == 0, a_2, a_4 != 0
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it.product(range(1), range(1, q), range(1), range(1, 2)),
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# a_1 == 0, a_4 == 0, a_3, a_2 != 0
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it.product(range(1), range(1, q), range(1, 2), range(1)),
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# a_2 == 0, a_3 == 0, a_1, a_4 != 0
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it.product(range(1, q), range(1), range(1), range(1, 2)),
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# a_2 == 0, a_4 == 0, a_1, a_3 != 0
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it.product(range(1, q), range(1), range(1, 2), range(1)),
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# a_3 == 0, a_4 == 0, a_1, a_2 != 0
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it.product(range(1, q), range(1, 2), range(1), range(1)),
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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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# print("\t\t\tMultiplication of the vector " + str(v_theta))
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large_sigma_for_this_vector = False
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for shift in range(1, q_4):
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# print("shift = " + str(shift) + ", q_4 = " + str(q_4))
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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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]
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for ranges in list_of_ranges:
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good_vectors, bad_vectors = cable.check_combinations_in_range(ranges)
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print("good_vectors : bad_vectors: " + str(len(good_vectors)) +\
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" : " + str(len(bad_vectors)))
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#
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# print("\ngood_vectors")
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# print(len(good_vectors))
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# print("\nbad_vectors")
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# print(len(bad_vectors))
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# print(bad_vectors)
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sigma_v = cable.calculate_sigma(shifted_theta)
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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large_sigma_for_this_vector = True
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break
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if large_sigma_for_this_vector:
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good_vectors.append(v_theta)
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pass
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else:
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bad_vectors.append(v_theta)
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large_sigma_for_last_theta_non_zero = False
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print("\ngood_vectors")
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print(len(good_vectors))
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print("\nbad_vectors")
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print(len(bad_vectors))
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print(bad_vectors)
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bad_vectors = []
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good_vectors = []
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large_sigma_for_last_theta_zero = True
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for vector in it.product(range(q_4), range(q_4)):
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v_theta = list(vector)
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v_theta.append(1)
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v_theta.append(0)
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a_1, a_2 = vector
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a_3 = 1
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a_4 = 0
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assert [a_1, a_2, a_3, a_4] == v_theta
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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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# print("\t\t\tMultiplication of the vector " + str(v_theta))
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large_sigma_for_this_vector = False
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for shift in range(1, q_4):
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# print("shift = " + str(shift) + ", q_4 = " + str(q_4))
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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 = cable.calculate_sigma(shifted_theta)
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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large_sigma_for_this_vector = True
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break
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if large_sigma_for_this_vector:
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good_vectors.append(v_theta)
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pass
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else:
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bad_vectors.append(v_theta)
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large_sigma_for_last_theta_zero = False
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# break
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print("\ngood_vectors")
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print(len(good_vectors))
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print("\nbad_vectors")
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print(len(bad_vectors))
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print(bad_vectors)
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bad_vectors = []
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good_vectors = []
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print("\n\nNic nie ma")
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for vector in range(q_4):
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v_theta = [vector]
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v_theta.append(1)
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v_theta.append(0)
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v_theta.append(last_theta)
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a_1 = vector
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a_2 = 1
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a_3 = 0
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a_4 = last_theta
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assert [a_1, a_2, a_3, a_4] == v_theta
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if a_1 == a_2 == a_3:
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if a_3 == 0:
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print("\na_1 == a_2 == a_3 == 0")
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continue
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elif a_3 == a_4:
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print("\nall a_i == a != 0")
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continue
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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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# print("\t\t\tMultiplication of the vector " + str(v_theta))
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large_sigma_for_this_vector = False
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for shift in range(1, q_4):
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# print("shift = " + str(shift) + ", q_4 = " + str(q_4))
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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 = cable.calculate_sigma(shifted_theta)
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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large_sigma_for_this_vector = True
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break
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if large_sigma_for_this_vector:
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good_vectors.append(v_theta)
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pass
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else:
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bad_vectors.append(v_theta)
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large_sigma_for_last_theta_zero = False
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# break
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if large_sigma_for_last_theta_non_zero and large_sigma_for_last_theta_zero:
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print(100 * "\n\nHURA HURA")
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print(knot_description)
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print("\ngood_vectors")
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print(len(good_vectors))
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print("\nbad_vectors")
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print(len(bad_vectors))
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print(bad_vectors)
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return None
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@ -648,11 +580,11 @@ def eval_cable_for_null_signature(knot_sum, print_results=False, verbose=None):
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null_combinations = 0
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zero_theta_combinations = []
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ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
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range_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
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if verbose:
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print()
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print(knot_description)
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for v_theta in it.product(*ranges_list):
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for v_theta in it.product(*range_list):
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if f(*v_theta, verbose=False).is_zero_everywhere():
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zero_theta_combinations.append(v_theta)
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m = len([theta for theta in v_theta if theta != 0])
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