cable class
This commit is contained in:
Maria Marchwicka
parent
afbda34111
commit
4cdb4622ab
@ -203,6 +203,248 @@ class SignatureFunction(object):
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return 2 * sum(before_arg) + cnt[arg]
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return 2 * sum(before_arg) + cnt[arg]
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class TorusCable(object):
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def __init__(self, knot_formula=None, k_vector=None, q_vector=None):
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# q_i = 2 * k_i + 1
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if knot_formula is None:
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knot_formula = config.knot_formula
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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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print("Please give a list of k (k_vector) or q values (q_vector).")
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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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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_description = get_knot_descrption(*self.knot_sum)
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self.sigma_function = None
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def is_sigma_for_vector_class_big(self, theta_vector):
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return True
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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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sigma_q_1 = get_untwisted_signature_function(k_1)
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sigma_q_2 = get_untwisted_signature_function(k_2)
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sigma_q_3 = get_untwisted_signature_function(k_3)
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def sigma_function(theta_vector):
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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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sigma_v = untwisted_part + twisted_part
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return sigma_v
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return sigma_function
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def calculate_sigma(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.__calculate_sigma(theta_vector)
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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 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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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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large_sigma_for_all_v_combinations = True
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bad_vectors = []
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good_vectors = []
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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, 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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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_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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def main(arg):
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def main(arg):
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if arg[1]:
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if arg[1]:
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limit = int(arg[1])
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limit = int(arg[1])
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@ -234,7 +476,7 @@ def search_for_large_signature_value(knot_formula=None,
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# iterate over q-vector
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# iterate over q-vector
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for c in combinations:
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for c in combinations:
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k = [(P.unrank(i) - 1)/2 for i in c]
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k = [(P.unrank(i + 2) - 1)/2 for i in c]
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if config.only_slice_candidates:
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if config.only_slice_candidates:
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if not (k[3] > 4 * k[2] and
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if not (k[3] > 4 * k[2] and
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k[2] > 4 * k[1] and
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k[2] > 4 * k[1] and
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@ -250,266 +492,6 @@ def search_for_large_signature_value(knot_formula=None,
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# searching for sigma > 5 + #(v_i != 0)
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def eval_cable_for_large_sigma(k_vector=None,
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knot_formula=None,
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print_results=True,
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verbose=None,
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q_vector=None):
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if knot_formula is None:
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knot_formula = config.knot_formula
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if verbose is None:
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verbose = config.verbose
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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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print("Please give a list of k (k_vector) or q values (q_vector).")
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return None
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else:
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k_vector = [(i - 1)/2 for i in q_vector]
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k = k_vector
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knot_sum = eval(knot_formula)
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if len(knot_sum) != 4:
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print("Wrong number of cable direct summands!")
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return None
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knot_description = get_knot_descrption(*knot_sum)
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return _eval_cable_for_large_sigma(k_vector, knot_description,
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print_results, verbose)
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def _eval_cable_for_large_sigma(k, knot_description, print_results, verbose):
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# k is a k_vector
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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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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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large_sigma_for_all_v_combinations = True
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bad_vectors = []
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good_vectors = []
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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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sigma_q_1 = get_untwisted_signature_function(k_1)
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sigma_q_2 = get_untwisted_signature_function(k_2)
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sigma_q_3 = get_untwisted_signature_function(k_3)
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# large_sigma_for_last_theta_non_zero = True
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#!!!!!!!!!!!!!!!!
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# consider a_4 non-zero and zero
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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(3 * [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, a_2, a_3 = 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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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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# "untwisted" part (Levine-Tristram signatures)
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a_1, a_2, a_3, a_4 = shifted_theta
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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(shifted_theta):
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if a:
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tp[i] = -q_4 + 2 * a - 2 * (a^2/q_4)
|
|
||||||
twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
|
|
||||||
# assert twisted_part == int(twisted_part)
|
|
||||||
|
|
||||||
sigma_v = untwisted_part + twisted_part
|
|
||||||
# print(knot_description + "\t" + str(shifted_theta) +\
|
|
||||||
# "\t" + str(sigma_v))
|
|
||||||
# + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
|
||||||
|
|
||||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
|
||||||
large_sigma_for_this_vector = True
|
|
||||||
|
|
||||||
if large_sigma_for_this_vector:
|
|
||||||
good_vectors.append(shifted_theta)
|
|
||||||
pass
|
|
||||||
else:
|
|
||||||
bad_vectors.append(shifted_theta)
|
|
||||||
large_sigma_for_last_theta_non_zero = False
|
|
||||||
|
|
||||||
last_theta = 0
|
|
||||||
large_sigma_for_last_theta_zero = True
|
|
||||||
for vector in it.product(3 * [range(q_4)]):
|
|
||||||
v_theta = list(vector)
|
|
||||||
v_theta.append(last_theta)
|
|
||||||
a_1, a_2, a_3 = vector
|
|
||||||
a_4 = last_theta
|
|
||||||
assert [a_1, a_2, a_3, a_4] == v_theta
|
|
||||||
if a_1 == a_2 == a_3:
|
|
||||||
if a_3 == 0:
|
|
||||||
print("\na_1 == a_2 == a_3 == 0")
|
|
||||||
continue
|
|
||||||
elif a_3 == a_4:
|
|
||||||
print("\nall a_i == a != 0")
|
|
||||||
continue
|
|
||||||
|
|
||||||
if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
|
|
||||||
continue
|
|
||||||
|
|
||||||
# print("\t\t\tMultiplication of the vector " + str(v_theta))
|
|
||||||
large_sigma_for_this_vector = False
|
|
||||||
for shift in range(1, q_4):
|
|
||||||
# print("shift = " + str(shift) + ", q_4 = " + str(q_4))
|
|
||||||
shifted_theta = [(shift * a) % q_4 for a in
|
|
||||||
[a_1, a_2, a_3, a_4]]
|
|
||||||
|
|
||||||
|
|
||||||
# "untwisted" part (Levine-Tristram signatures)
|
|
||||||
a_1, a_2, a_3, a_4 = shifted_theta
|
|
||||||
untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
|
|
||||||
sigma_q_2(ksi * a_2) +
|
|
||||||
sigma_q_3(ksi * a_3) -
|
|
||||||
sigma_q_3(ksi * a_4) +
|
|
||||||
sigma_q_1(ksi * a_1 * 2) -
|
|
||||||
sigma_q_1(ksi * a_4 * 2))
|
|
||||||
|
|
||||||
# "twisted" part
|
|
||||||
tp = [0, 0, 0, 0]
|
|
||||||
for i, a in enumerate(shifted_theta):
|
|
||||||
if a:
|
|
||||||
tp[i] = -q_4 + 2 * a - 2 * (a^2/q_4)
|
|
||||||
twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
|
|
||||||
# assert twisted_part == int(twisted_part)
|
|
||||||
|
|
||||||
sigma_v = untwisted_part + twisted_part
|
|
||||||
# print(knot_description + "\t" + str(shifted_theta) +\
|
|
||||||
# "\t" + str(sigma_v))
|
|
||||||
# + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
|
||||||
|
|
||||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
|
||||||
large_sigma_for_this_vector = True
|
|
||||||
# break
|
|
||||||
# else:
|
|
||||||
# pass
|
|
||||||
# print(knot_description + "\t" + \
|
|
||||||
# str(shifted_theta) +\
|
|
||||||
# "\t" + str(sigma_v))
|
|
||||||
|
|
||||||
|
|
||||||
if large_sigma_for_this_vector:
|
|
||||||
good_vectors.append(shifted_theta)
|
|
||||||
pass
|
|
||||||
# print("large_sigma_for_this_vector\n\n\n\n")
|
|
||||||
# print("\n\nHURA HURA")
|
|
||||||
else:
|
|
||||||
# print(shifted_theta)
|
|
||||||
# if a_3 == a_4:
|
|
||||||
# print(sigma_q_1(ksi * a_4 * 2))
|
|
||||||
bad_vectors.append(shifted_theta)
|
|
||||||
large_sigma_for_last_theta_zero = False
|
|
||||||
# break
|
|
||||||
|
|
||||||
if large_sigma_for_last_theta_non_zero and large_sigma_for_last_theta_zero:
|
|
||||||
print(100 * "\n\nHURA HURA")
|
|
||||||
print(knot_description)
|
|
||||||
|
|
||||||
# # if config.print_calculations_for_large_sigma:
|
|
||||||
# # print("*" * 100)
|
|
||||||
# # print("\n\nLarge signature value\n")
|
|
||||||
# # print(knot_description)
|
|
||||||
# # print("\nv_theta: ", end="")
|
|
||||||
# # print(v_theta)
|
|
||||||
# # print("k values: ", end="")
|
|
||||||
# # print(str(k_1) + " " + str(k_2) + " " + \
|
|
||||||
# # str(k_3) + " " + str(k_4))
|
|
||||||
# # print(condition)
|
|
||||||
# # print("non zero value in v_theta: " + \
|
|
||||||
# # str(np.count_nonzero(v_theta)))
|
|
||||||
# # print("sigma_v: " + str(sigma_v))
|
|
||||||
# # print("\ntwisted_part: ", end="")
|
|
||||||
# # print(twisted_part)
|
|
||||||
# # print("untwisted_part: ", end="")
|
|
||||||
# # print(untwisted_part)
|
|
||||||
# # print("\n\nCALCULATIONS")
|
|
||||||
# # print("*" * 100)
|
|
||||||
# # sults_LT(v_theta, knot_description,
|
|
||||||
# # ksi, untwisted_part,
|
|
||||||
# # k, sigma_q_1, sigma_q_2, sigma_q_3)
|
|
||||||
# # sults_sigma(v_theta, knot_description, tp, q_4)
|
|
||||||
# # print("*" * 100 + "\n" * 5)
|
|
||||||
# # else:
|
|
||||||
# # print(knot_description + "\t" + str(v_theta) +\
|
|
||||||
# # "\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
|
||||||
# # # if config.stop_after_firts_large_sigma:
|
|
||||||
# # # break
|
|
||||||
# # # sigma is small
|
|
||||||
# # else:
|
|
||||||
# # if config.print_calculations_for_small_sigma:
|
|
||||||
# # print("\n" * 5 + "*" * 100)
|
|
||||||
# # print("\nSmall signature value\n")
|
|
||||||
# # print(knot_description)
|
|
||||||
# # print_results_LT(v_theta, knot_description, ksi, untwisted_part,
|
|
||||||
# # k, sigma_q_1, sigma_q_2, sigma_q_3)
|
|
||||||
# # print_results_sigma(v_theta, knot_description, tp, q_4)
|
|
||||||
# # print("*" * 100 + "\n" * 5)
|
|
||||||
# # large_sigma_for_all_v_combinations = False
|
|
||||||
# #
|
|
||||||
# # if not config.print_calculations_for_small_sigma:
|
|
||||||
# # print(knot_description + "\t" + str(v_theta) +\
|
|
||||||
# # "\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
|
||||||
# #
|
|
||||||
# #
|
|
||||||
# # # print("ojojojoj")
|
|
||||||
# # # break
|
|
||||||
#
|
|
||||||
# if large_sigma_for_all_v_combinations:
|
|
||||||
# print("\n\n\nHura hura")
|
|
||||||
# good_knots.append((knot_description, v_theta))
|
|
||||||
#
|
|
||||||
# # else:
|
|
||||||
# # print "\n\tSmall signature value"
|
|
||||||
# # print knot_description
|
|
||||||
# # print "v_theta: " + str(v_theta)
|
|
||||||
# # print condition
|
|
||||||
# # print "non zero value in v_theta: " + str(np.count_nonzero(v_theta))
|
|
||||||
# # print "signature at 1/2: " + str(y)
|
|
||||||
print("\ngood_vectors")
|
|
||||||
print(good_vectors)
|
|
||||||
print("\nbad_vectors")
|
|
||||||
print(bad_vectors)
|
|
||||||
return None
|
|
||||||
|
|
||||||
|
|
||||||
def print_results_LT(v_theta, knot_description, ksi, untwisted_part,
|
def print_results_LT(v_theta, knot_description, ksi, untwisted_part,
|
||||||
k, sigma_q_1, sigma_q_2, sigma_q_3):
|
k, sigma_q_1, sigma_q_2, sigma_q_3):
|
||||||
a_1, a_2, a_3, a_4 = v_theta
|
a_1, a_2, a_3, a_4 = v_theta
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user