end of implementation for large gignature
This commit is contained in:
Maria Marchwicka
parent
1ec26c1b55
commit
ac1a1d3475
@ -27,6 +27,17 @@ 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_untwisted_signature_function(self, 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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w = ([((2 * a + 1)/(2 * q), -1 * sgn(j)) for a in range(k)] +
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[((2 * a + 1)/(2 * q), 1 * sgn(j))
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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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@ -63,6 +74,9 @@ class TorusCable(object):
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return signature_as_function_of_theta(*(len_a * [0]))
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if len_t != len_a:
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if len(thetas[0]) == len_a:
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thetas = thetas[0]
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else:
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msg = "This function takes exactly " + str(len_a) + \
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" arguments or no argument at all (" + str(len_t) + \
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" given)."
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@ -73,7 +87,7 @@ class TorusCable(object):
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# for each cable knot in cable sum apply theta
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for i, knot in enumerate(self.knot_sum):
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try:
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ssf = get_signature_summand_as_theta_function(*knot)
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ssf = get_summand_signature_as_theta_function(*knot)
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sf += ssf(thetas[i])
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# in case wrong theata value was given
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except ValueError as e:
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@ -102,6 +116,94 @@ 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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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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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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def s__check_combinations_in_range(self, range_product):
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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_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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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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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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@ -114,6 +216,7 @@ class TorusCable(object):
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print(self.knot_description)
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print("Zero cases: " + str(number_of_null_comb))
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print("All cases: " + str(number_of_all_comb))
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if list_of_good_vectors:
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print("Zero theta combinations: ")
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for el in list_of_good_vectors:
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print(el)
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@ -124,8 +227,9 @@ class TorusCable(object):
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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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q_4 = self.q_vector[-1]
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k_4 = self.k_vector[-1]
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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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@ -147,9 +251,6 @@ class TorusCable(object):
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print("\n")
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def __tmp_get_max_sigma_for_vector_class(self, theta_vector):
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# print("\n")
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# print(self.knot_description)
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# print("vector = " + str(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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@ -159,13 +260,8 @@ class TorusCable(object):
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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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max_sigma = (shifted_theta, sigma)
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assert max_sigma[1] == 0, knot_description
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# print("\n" + self.knot_description + "\t" + str(max_sigma[0]) +\
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# "\t" + str(max_sigma[1]))
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return max_sigma[1]
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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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@ -175,9 +271,9 @@ class TorusCable(object):
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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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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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@ -208,9 +304,9 @@ class TorusCable(object):
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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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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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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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print("\n\nLevine-Tristram signatures for the cable sum: ")
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print(knot_description)
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print("and characters:\n" + str(theta_vector) + ",")
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@ -335,10 +431,8 @@ 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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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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@ -346,19 +440,12 @@ class TorusCable(object):
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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 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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# 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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# if len(bad_vectors) > 8:
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# break
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print(len(bad_vectors))
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if a_1 and a_2 and a_3 and a_4:
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assert len(bad_vectors) % 8 == 0
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return good_vectors, bad_vectors
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# searching for sigma > 5 + #(v_i != 0)
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@ -369,7 +456,7 @@ class TorusCable(object):
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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=True):
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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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@ -379,8 +466,6 @@ class TorusCable(object):
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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 len(all_bad_vectors) > 8:
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break
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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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@ -392,11 +477,6 @@ class TorusCable(object):
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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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# if len(all_bad_vectors) < 8:
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# print()
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# print(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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@ -405,11 +485,7 @@ class TorusCable(object):
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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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if print_results:
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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(self.knot_description, end="\t\t\t")
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# print()
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if self.__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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@ -459,16 +535,16 @@ class SignatureFunction(object):
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counter[mod_one(2 * jump_arg)] = jump
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return SignatureFunction(counter=counter)
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def __lshift__(self, shift):
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# A shift of the signature functions corresponds to the rotation.
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return self.__rshift__(-shift)
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def __rshift__(self, shift):
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# A shift of the signature functions corresponds to the rotation.
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new_data = []
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for jump_arg, jump in self.cnt_signature_jumps.items():
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new_data.append((mod_one(jump_arg + shift), jump))
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return SignatureFunction(values=new_data)
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def __lshift__(self, shift):
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return self.__rshift__(-shift)
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def __neg__(self):
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counter = collections.Counter()
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counter.subtract(self.cnt_signature_jumps)
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@ -498,16 +574,33 @@ class SignatureFunction(object):
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return result[:-2] + "."
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def __call__(self, arg):
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# Compute the value of the signature function at the point arg.
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# This requires summing all signature jumps that occur before arg.
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# return the value of the signature function at the point arg, i.e.
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# sum of all signature jumps that occur before arg
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arg = mod_one(arg)
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cnt = self.cnt_signature_jumps
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before_arg = [jump for jump_arg, jump in cnt.items() if jump_arg < arg]
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return 2 * sum(before_arg) + cnt[arg]
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def is_big(self):
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max = 0
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items = self.cnt_signature_jumps.items()
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for arg, _ in items:
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current = sum([jump for jump_arg, jump in items if jump_arg <= arg])
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if abs(current) > abs(max):
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max = current
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if abs(max) > 9:
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return max
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return max
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def mod_one(n):
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return n - floor(n)
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def get_untwisted_signature_function(j):
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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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@ -517,15 +610,16 @@ def get_untwisted_signature_function(j):
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return SignatureFunction(values=w)
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def get_signature_summand_as_theta_function(*arg):
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def get_signture_function(theta):
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def get_summand_signature_as_theta_function(*arg):
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def get_summand_signture_function(theta):
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# TBD: another formula (for t^2) description
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k_n = abs(arg[-1])
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if theta > k_n:
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msg = "k for the pattern in the cable is " + str(arg[-1]) + \
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". Parameter theta should not be larger than abs(k)."
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raise ValueError(msg)
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pass
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# print(msg)
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# raise ValueError(msg)
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# twisted part
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cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
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@ -546,8 +640,8 @@ def get_signature_summand_as_theta_function(*arg):
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test2 = -c + b
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assert test == test
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return cable_signature
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get_signture_function.__doc__ = get_signture_function_docsting
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return get_signture_function
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get_summand_signture_function.__doc__ = get_summand_signture_function_docsting
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return get_summand_signture_function
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def get_blanchfield_for_pattern(k_n, theta):
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@ -580,15 +674,17 @@ def get_blanchfield_for_pattern(k_n, theta):
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return SignatureFunction(values=results)
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def get_signature_summand_as_theta_function(*arg):
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def get_signture_function(theta):
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def get_summand_signature_as_theta_function(*arg):
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def get_summand_signture_function(theta):
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# TBD: another formula (for t^2) description
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k_n = abs(arg[-1])
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if theta > k_n:
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msg = "k for the pattern in the cable is " + str(arg[-1]) + \
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". Parameter theta should not be larger than abs(k)."
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raise ValueError(msg)
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pass
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# print(msg)
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# raise ValueError(msg)
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# twisted part
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cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
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@ -609,8 +705,8 @@ def get_signature_summand_as_theta_function(*arg):
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test2 = -c + b
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assert test == test
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return cable_signature
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get_signture_function.__doc__ = get_signture_function_docsting
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return get_signture_function
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get_summand_signture_function.__doc__ = get_summand_signture_function_docsting
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return get_summand_signture_function
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def get_untwisted_signature_function(j):
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@ -733,12 +829,12 @@ SignatureFunction.__doc__ = \
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signature functions as defined on the interval [0,1).
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"""
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get_signture_function_docsting = \
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get_summand_signture_function_docsting = \
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"""
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This function returns SignatureFunction for previously defined single
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cable T_(2, q) and a theta given as an argument.
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The cable was defined by calling function
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get_signature_summand_as_theta_function(*arg)
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get_summand_signature_as_theta_function(*arg)
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with the cable description as an argument.
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It is an implementaion of the formula:
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Bl_theta(K'_(2, d)) =
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@ -785,7 +881,7 @@ get_blanchfield_for_pattern.__doc__ = \
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(https://arxiv.org/pdf/1809.08791.pdf)
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"""
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get_signature_summand_as_theta_function.__doc__ = \
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get_summand_signature_as_theta_function.__doc__ = \
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"""
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Argument:
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n integers that encode a single cable, i.e.
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@ -1,7 +1,6 @@
|
||||
#!/usr/bin/python
|
||||
|
||||
# TBD: read about Factory Method, variable in docstring, sage documentation
|
||||
# move settings to sep file
|
||||
|
||||
import os
|
||||
import sys
|
||||
@ -13,7 +12,7 @@ import re
|
||||
# os.system('sage --preparse cable_signature.sage')
|
||||
# os.system('mv cable_signature.sage.py cable_signature.py')
|
||||
# from cable_signature import SignatureFunction, TorusCable
|
||||
#
|
||||
|
||||
|
||||
class Config(object):
|
||||
def __init__(self):
|
||||
@ -42,115 +41,58 @@ class Config(object):
|
||||
self.verbose = False
|
||||
|
||||
self.print_results = True
|
||||
self.print_results = False
|
||||
# self.print_results = False
|
||||
|
||||
self.print_calculations_for_large_sigma = True
|
||||
self.print_calculations_for_large_sigma = False
|
||||
|
||||
# is the ratio restriction for values in k_vector taken into account
|
||||
# False flag is usefull to make quick script tests
|
||||
# is the ratio restriction for values in q_vector taken into account
|
||||
self.only_slice_candidates = True
|
||||
self.only_slice_candidates = False
|
||||
|
||||
|
||||
# range for a_i, v = [a_1, a_2, a_3, a_4], for sigma calculations
|
||||
def get_list_of_ranges(self, q):
|
||||
# upper bound supposed to be ub = k + 1
|
||||
def get_list_of_ranges(self, ub):
|
||||
list_of_ranges = [
|
||||
# all characters a_1, a_2, a_3, a_4 != 0
|
||||
it.product(range(1, q), range(1, q), range(1, q), range(1, 2)),
|
||||
it.product(range(1, ub), range(1, ub), range(1, ub), range(1, 2)),
|
||||
|
||||
# a_1 == 0, a_2, a_3, a_4 != 0
|
||||
it.product(range(1), range(1, q), range(1, q), range(1, 2)),
|
||||
it.product(range(1), range(1, ub), range(1, ub), range(1, 2)),
|
||||
# a_2 == 0, a_1, a_3, a_4 != 0
|
||||
it.product(range(1, q), range(1), range(1, q), range(1, 2)),
|
||||
it.product(range(1, ub), range(1), range(1, ub), range(1, 2)),
|
||||
# a_3 == 0, a_1, a_2, a_4 != 0
|
||||
it.product(range(1, q), range(1, q), range(1), range(1, 2)),
|
||||
it.product(range(1, ub), range(1, ub), range(1), range(1, 2)),
|
||||
# a_4 == 0, a_1, a_2, a_3 != 0
|
||||
it.product(range(1, q), range(1, q), range(1, 2), range(1)),
|
||||
it.product(range(1, ub), range(1, ub), range(1, 2), range(1)),
|
||||
|
||||
# a_1 == 0, a_2 == 0, a_3, a_4 != 0
|
||||
it.product(range(1), range(1), range(1, q), range(1, 2)),
|
||||
it.product(range(1), range(1), range(1, ub), range(1, 2)),
|
||||
# a_1 == 0, a_3 == 0, a_2, a_4 != 0
|
||||
it.product(range(1), range(1, q), range(1), range(1, 2)),
|
||||
it.product(range(1), range(1, ub), range(1), range(1, 2)),
|
||||
# a_1 == 0, a_4 == 0, a_3, a_2 != 0
|
||||
it.product(range(1), range(1, q), range(1, 2), range(1)),
|
||||
it.product(range(1), range(1, ub), range(1, 2), range(1)),
|
||||
# a_2 == 0, a_3 == 0, a_1, a_4 != 0
|
||||
it.product(range(1, q), range(1), range(1), range(1, 2)),
|
||||
it.product(range(1, ub), range(1), range(1), range(1, 2)),
|
||||
# a_2 == 0, a_4 == 0, a_1, a_3 != 0
|
||||
it.product(range(1, q), range(1), range(1, 2), range(1)),
|
||||
it.product(range(1, ub), range(1), range(1, 2), range(1)),
|
||||
# a_3 == 0, a_4 == 0, a_1, a_2 != 0
|
||||
it.product(range(1, q), range(1, 2), range(1), range(1)),
|
||||
it.product(range(1, ub), range(1, 2), range(1), range(1)),
|
||||
]
|
||||
|
||||
list_of_ranges =
|
||||
[
|
||||
# all characters a_1, a_2, a_3, a_4 != 0
|
||||
# 1, 1, 1, 1
|
||||
it.product(range(1, 2), range(1, 2), range(1, 2), range(1, 2)),
|
||||
|
||||
# -1, -1, -1, 1
|
||||
it.product(range(q - 1, q), range(q - 1, q), range(q - 1, q), \
|
||||
range(1, 2)),
|
||||
|
||||
# 1, -1, -1, 1
|
||||
it.product(range(1, 2), range(q - 1, q), range(q - 1, q), \
|
||||
range(1, 2)),
|
||||
# -1 , -1, 1, 1
|
||||
it.product(range(q - 1, q), range(q - 1, q), range(1, 2), \
|
||||
range(1, 2)),
|
||||
# -1, 1, -1, 1
|
||||
it.product(range(q - 1, q), range(1, 2), range(q - 1, q), \
|
||||
range(1, 2)),
|
||||
# 1, 1, -1, 1
|
||||
it.product(range(1, 2), range(1, 2), range(q - 1, q), \
|
||||
range(1, 2)),
|
||||
# 1, -1, 1, 1
|
||||
it.product(range(1, 2), range(q - 1, q), range(1, 2), \
|
||||
range(1, 2)),
|
||||
# -1, 1, 1, 1
|
||||
it.product(range(q - 1, q), range(1, 2), range(1, 2), \
|
||||
range(1, 2)),
|
||||
]
|
||||
|
||||
return list_of_ranges
|
||||
|
||||
|
||||
|
||||
|
||||
def main(arg):
|
||||
if arg[1]:
|
||||
try:
|
||||
limit = int(arg[1])
|
||||
else:
|
||||
except IndexError:
|
||||
limit = None
|
||||
knots_with_large_sigma = search_for_large_signature_value(limit=limit)
|
||||
search_for_large_signature_value(limit=limit)
|
||||
knots_with_large_sigma = search_for_large_sigma_value(limit=limit)
|
||||
# search_for_null_signature_value(limit=limit)
|
||||
|
||||
# searching for sigma > 5 + #(v_i != 0) over given knot schema
|
||||
def __search_for_large_signature_value(knot_formula, limit,
|
||||
verbose, print_results):
|
||||
# number of k_i (q_i) variables to substitute
|
||||
k_size = extract_max(knot_formula) + 1
|
||||
combinations = it.combinations_with_replacement(range(0, limit + 1), k_size)
|
||||
P = Primes()
|
||||
good_knots = []
|
||||
# iterate over q-vector
|
||||
for c in combinations:
|
||||
q = list(c)
|
||||
q[0] = P.unrank(q[0] + 1 + config.start_shift)
|
||||
q[1] = P.next(q[0] * 4 + q[1])
|
||||
q[2] = P.next(q[1] * 4 + q[2])
|
||||
q[3] = P.next(q[2] * 4 + q[3])
|
||||
cable = TorusCable(knot_formula=knot_formula, q_vector=q)
|
||||
list_of_ranges = config.get_list_of_ranges(cable.q_vector[-1])
|
||||
print(cable.knot_description)
|
||||
if cable.eval_cable_for_large_sigma(list_of_ranges, verbose=verbose,
|
||||
print_results=print_results):
|
||||
good_knots.append(cable)
|
||||
return good_knots
|
||||
|
||||
# searching for sigma > 5 + #(v_i != 0) over given knot schema
|
||||
def search_for_large_signature_value(knot_formula=None, limit=None,
|
||||
verbose=None, print_results=None):
|
||||
def set_parameters(knot_formula, limit, verbose, print_results):
|
||||
if limit is None:
|
||||
limit = config.limit
|
||||
if knot_formula is None:
|
||||
@ -159,12 +101,19 @@ def search_for_large_signature_value(knot_formula=None, limit=None,
|
||||
vebose = config.verbose
|
||||
if print_results is None:
|
||||
print_results = config.print_results
|
||||
return knot_formula, limit, verbose, print_results
|
||||
|
||||
|
||||
|
||||
# searching for sigma > 5 + #(v_i != 0) over given knot schema
|
||||
def search_for_large_sigma_value(knot_formula=None, limit=None,
|
||||
verbose=None, print_results=None):
|
||||
|
||||
knot_formula, limit, verbose, print_results = \
|
||||
set_parameters(knot_formula, limit, verbose, print_results)
|
||||
|
||||
k_vector_size = extract_max(knot_formula) + 1
|
||||
limit = max(limit, k_vector_size)
|
||||
if config.only_slice_candidates:
|
||||
return __search_for_large_signature_value(knot_formula, limit, verbose,
|
||||
print_results)
|
||||
|
||||
# number of k_i (q_i) variables to substitute
|
||||
combinations = it.combinations(range(1, limit + 1), k_vector_size)
|
||||
@ -173,23 +122,27 @@ def search_for_large_signature_value(knot_formula=None, limit=None,
|
||||
|
||||
# iterate over q-vector
|
||||
for c in combinations:
|
||||
k = [(P.unrank(i + config.start_shift) - 1)/2 for i in c]
|
||||
cable = TorusCable(knot_formula=knot_formula, k_vector=k)
|
||||
list_of_ranges = config.get_list_of_ranges(cable.q_vector[-1])
|
||||
print(cable.knot_description)
|
||||
q = [P.unrank(i + config.start_shift) for i in c]
|
||||
if config.only_slice_candidates:
|
||||
if not (q[3] > 4 * q[2] and
|
||||
q[2] > 4 * q[1] and
|
||||
q[1] > 4 * q[0]):
|
||||
if verbose:
|
||||
print("Ratio-condition does not hold")
|
||||
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,
|
||||
print_results=print_results):
|
||||
good_knots.append(cable)
|
||||
good_knots.append(cable.knot_description)
|
||||
return good_knots
|
||||
|
||||
# searching for signature == 0
|
||||
def search_for_null_signature_value(knot_formula=None, limit=None):
|
||||
if limit is None:
|
||||
limit = config.limit
|
||||
if knot_formula is None:
|
||||
knot_formula = config.knot_formula
|
||||
print_results = config.print_results
|
||||
verbose = config.verbose
|
||||
def search_for_null_signature_value(knot_formula=None, limit=None,
|
||||
verbose=None, print_results=None):
|
||||
|
||||
knot_formula, limit, verbose, print_results = \
|
||||
set_parameters(knot_formula, limit, verbose, print_results)
|
||||
|
||||
k_vector_size = extract_max(knot_formula) + 1
|
||||
combinations = it.combinations_with_replacement(range(1, limit + 1),
|
||||
@ -210,11 +163,57 @@ def search_for_null_signature_value(knot_formula=None, limit=None):
|
||||
str(all_comb) + "\n")
|
||||
f_results.write(line)
|
||||
|
||||
# searching for signature > 5 + #(v_i != 0) over given knot schema
|
||||
def search_for_large_signature_value(knot_formula=None, limit=None,
|
||||
verbose=None, print_results=None):
|
||||
|
||||
knot_formula, limit, verbose, print_results = \
|
||||
set_parameters(knot_formula, limit, verbose, print_results)
|
||||
|
||||
k_vector_size = extract_max(knot_formula) + 1
|
||||
combinations = it.combinations(range(1, limit + 1), k_vector_size)
|
||||
P = Primes()
|
||||
good_knots = []
|
||||
|
||||
# iterate over q-vector
|
||||
for c in combinations:
|
||||
q = [P.unrank(i + config.start_shift) for i in c]
|
||||
if config.only_slice_candidates:
|
||||
if not (q[3] > 4 * q[2] and
|
||||
q[2] > 4 * q[1] and
|
||||
q[1] > 4 * q[0]):
|
||||
if verbose:
|
||||
print("Ratio-condition does not hold")
|
||||
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,
|
||||
print_results=print_results):
|
||||
good_knots.append(cable.knot_description)
|
||||
|
||||
return good_knots
|
||||
|
||||
|
||||
|
||||
|
||||
def get_shifted_combination(combination):
|
||||
# for now applicable only for schama
|
||||
# "[[k[0], k[1], k[2]], [k[3], k[4]],
|
||||
# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
|
||||
# shift the combination so that the knot can be a candidate for slice
|
||||
combination = [combination[0], 4 * combination[0] + combination[1],
|
||||
4 * (4 * combination[0] + combination[1]) + combination[2],
|
||||
4 * combination[0] + combination[3],
|
||||
4 * (4 * combination[0] + combination[3]) + combination[4]]
|
||||
return combination
|
||||
|
||||
|
||||
def extract_max(string):
|
||||
numbers = re.findall('\d+', string)
|
||||
numbers = map(int, numbers)
|
||||
return max(numbers)
|
||||
|
||||
|
||||
def is_trivial_combination(knot_sum):
|
||||
# for now is applicable only for schema that are sums of 4 cables
|
||||
if len(knot_sum) == 4:
|
||||
|
||||
Loading…
Reference in New Issue
Block a user