First knot with big signatures. Many fragments are doubled - will be deleted now
This commit is contained in:
Maria Marchwicka
parent
8ddb06fdb8
commit
c64382b5c7
@ -632,8 +632,8 @@ class TorusCable(object):
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# print(theta, end=" ")
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# print(theta, end=" ")
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# print(sum)
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# print(sum)
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if sum.is_integer():
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if sum.is_integer():
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print("#" * 100)
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# print("#" * 100)
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print(theta)
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# print(theta)
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return True
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return True
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return False
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return False
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# if self.is_value_for_vector_class_big(vector, sigma_or_sign):
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# if self.is_value_for_vector_class_big(vector, sigma_or_sign):
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191
main.sage
191
main.sage
@ -1,6 +1,6 @@
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#!/usr/bin/python
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#!/usr/bin/python
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attach("cable_signature.sage")
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attach("cable_signature.sage")
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attach("my_signature.sage")
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# attach("my_signature.sage")
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import numpy as np
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import numpy as np
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@ -35,36 +35,57 @@ def main():
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cable = cab_1 + cab_2
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cable = cab_1 + cab_2
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joined_formula = cable.knot_formula
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joined_formula = cable.knot_formula
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def check_all_thetas(cable):
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def is_big_in_ranges(cable, ranges_list):
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upper_bounds = cable.last_k_list[:4]
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we_have_no_problem = True
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# upper_bounds += [0, 0, 0, 0]
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ranges_list = [range(1, i + 1) for i in upper_bounds]
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ranges_list += [range(0, 1) for _ in range(4)]
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print(ranges_list)
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for theta in it.product(*ranges_list):
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for theta in it.product(*ranges_list):
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# pass
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if all(i == 0 for i in theta):
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continue
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we_have_a_problem = True
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if cable.is_metaboliser(theta):
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if cable.is_metaboliser(theta):
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print("\n" * 10)
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# print("\n" * 10)
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print("!" * 100)
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for shift in range(1, cable.q_order):
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for shift in range(1, cable.q_order):
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shifted_theta = [(shift * th) % cable.last_q_list[i]
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shifted_theta = [(shift * th) % cable.last_q_list[i]
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for i, th in enumerate(theta)]
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for i, th in enumerate(theta)]
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shifted_theta = [min(th, cable.last_q_list[i] - th)
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shifted_theta = [min(th, cable.last_q_list[i] - th)
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for i, th in enumerate(shifted_theta)]
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for i, th in enumerate(shifted_theta)]
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print(shifted_theta)
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sf = cable.signature_as_function_of_theta(*shifted_theta)
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sf = cable.signature_as_function_of_theta(*shifted_theta)
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extremum = abs(sf.extremum())
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extremum = abs(sf.extremum())
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if shift > 1:
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print(shifted_theta, end=" ")
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print(extremum)
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print(extremum)
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if extremum > 5 + np.count_nonzero(shifted_theta):
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if extremum > 5 + np.count_nonzero(shifted_theta):
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print("ok")
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# print("ok")
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we_have_a_problem = False
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break
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break
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else:
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elif shift == 1:
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print("hliphlip")
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print("*" * 10)
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print("!" * 100)
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print(shifted_theta, end=" ")
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print("\n" * 10)
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print(extremum)
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return
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if we_have_a_problem:
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we_have_a_big_problem = True
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break
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if not we_have_no_problem:
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print("we have a big problem")
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return we_have_no_problem
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def check_all_thetas(cable):
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upper_bounds = cable.last_k_list[:3]
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ranges_list = [range(0, i + 1) for i in upper_bounds]
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ranges_list.append(range(0, 2))
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ranges_list += [range(0, 1) for _ in range(4)]
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if not is_big_in_ranges(cable, ranges_list):
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return False
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upper_bounds = cable.last_k_list[5:8]
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ranges_list = [range(0, 1) for _ in range(4)]
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ranges_list += [range(0, i + 1) for i in upper_bounds]
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ranges_list.append(range(0, 2))
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if not is_big_in_ranges(cable, ranges_list):
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return False
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return True
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def get_q_vector(q_vector_size, lowest_number=1):
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def get_q_vector(q_vector_size, lowest_number=1):
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@ -83,139 +104,9 @@ def get_q_vector(q_vector_size, lowest_number=1):
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q[i] = next_number
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q[i] = next_number
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next_number = P.next(lowest_number)
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next_number = P.next(lowest_number)
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q = [P.unrank(i + config.start_shift) for i in c]
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q = [P.unrank(i) for i in c]
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ratio = q[3] > 4 * q[2] and q[2] > 4 * q[1] and q[1] > 4 * q[0]
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ratio = q[3] > 4 * q[2] and q[2] > 4 * q[1] and q[1] > 4 * q[0]
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if not ratio:
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if not ratio:
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# print("Ratio-condition does not hold")
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# print("Ratio-condition does not hold")
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continue
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continue
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print("q = ", q)
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print("q = ", q)
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# cable = TorusCable(knot_formula=knot_formula, q_vector=q)
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# list_of_ranges = config.get_list_of_ranges(cable.q_order)
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# if cable.eval_cable_for_large_values(list_of_ranges, SIGMA,
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# verbose=verbose,
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# print_results=print_results):
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# good_knots.append(cable.knot_description)
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# return good_knots
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# cab_to_update.update(cab_to_add)
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# cab_to_update.update(cab_to_add)
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# cab_to_update.update(cab_to_add)
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# cab_to_update.update(cab_to_add)
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pass
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#
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# def get_blanchfield_for_pattern(k_n, theta):
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# if theta == 0:
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# sf = TorusCable.get_untwisted_signature_function(k_n)
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# return sf.square_root() + sf.minus_square_root()
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#
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# results = []
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# k = abs(k_n)
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# ksi = 1/(2 * k + 1)
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#
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# # print("lambda_odd, i.e. (theta + e) % 2 != 0")
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# for e in range(1, k + 1):
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# if (theta + e) % 2 != 0:
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# results.append((e * ksi, 1 * sgn(k_n)))
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# results.append((1 - e * ksi, -1 * sgn(k_n)))
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# # print("\nlambda_even")
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# # print("\nnormal")
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# results_odd = results
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# results = []
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# for e in range(1, theta):
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# if (theta + e) % 2 == 0:
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# results.append((e * ksi, 1 * sgn(k_n)))
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# results.append((1 - e * ksi, -1 * sgn(k_n)))
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# # print(results)
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# results_even_small = results
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# results = []
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# # print("reversed")
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# for e in range(theta + 1, k + 1):
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# if (theta + e) % 2 == 0:
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# results.append((e * ksi, -1 * sgn(k_n)))
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# results.append((1 - e * ksi, 1 * sgn(k_n)))
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# # print(results)
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# results_even_big = results
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#
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# return results_odd, results_even_small, results_even_big
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# # return SignatureFunction(values=results)
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#
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# def main():
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# prim = 3
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# P = Primes()
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# for it in range(20):
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# prim = P.next(prim)
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# k_j = (prim - 1)/2
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# print(60 * "*")
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# print("k is " + str(k_j))
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# print(60 * "*")
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#
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# for i in range(1, k_j + 1):
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#
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# a, j, m = get_blanchfield_for_pattern(k_j, i)
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# sf_j = SignatureFunction(j)
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# sf_a = SignatureFunction(a)
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# sf_m = SignatureFunction(m)
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# sf_jam = sf_j + sf_a + sf_m
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# assert TorusCable.get_blanchfield_for_pattern(k_j, i) == sf_jam
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# af, jf, mf = get_blanchfield_for_pattern(-k_j, prim - i)
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# print(60 * "*")
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# print("lists")
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# print(af)
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# print(jf)
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# print(mf)
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# j = SignatureFunction(jf)
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# a = SignatureFunction(af)
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# m = SignatureFunction(mf)
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# minus_jam = j + a + m
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# values = cmp_blanchfield_for_pattern(-k_j, prim - i)
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# print("sum of lists - 3 lists added")
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# print(sorted(jf + af + mf))
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#
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# print("sum of lists - all values from Blanchfield")
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# print(sorted(values))
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#
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# assert values == af + jf + mf
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# print("not equeles - sf from all values")
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#
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# print(SignatureFunction(values))
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# print("not equeles - sum of sf")
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# print("sf for each list sep")
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# print("jf")
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# print(jf)
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# print("af")
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# print(af)
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# print("mf")
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# print(mf)
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# print("sum of abouve sfs")
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# print(minus_jam)
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# assert TorusCable.get_blanchfield_for_pattern(-k_j, prim - i) == \
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# SignatureFunction(values)
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# assert TorusCable.get_blanchfield_for_pattern(-k_j, prim - i) == \
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# minus_jam
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#
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#
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# # a, j, m = get_blanchfield_for_pattern(k_j, 2 * k_j + 1 - i)
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# # j = SignatureFunction(j)
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# # a = SignatureFunction(a)
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# # m = SignatureFunction(m)
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#
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# print("*" * 100)
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# print("i is " + str(i) + ", q is " + str(2 * k_j + 1), " q - i is " + str(2 * k_j + 1 - i))
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# print("*" * 100)
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#
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# ajm = sf_j + sf_a + sf_m
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# ajm_minus = a + j + m
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# print("4 times")
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# print(ajm + ajm + ajm_minus + ajm_minus)
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# print("is big")
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# print((ajm + ajm + ajm_minus + ajm_minus).is_big())
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# print()
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