First knot with big signatures. Many fragments are doubled - will be deleted now

This commit is contained in:
Maria Marchwicka 2020-10-14 18:50:21 +02:00
parent 8ddb06fdb8
commit c64382b5c7
2 changed files with 44 additions and 153 deletions

View File

@ -632,8 +632,8 @@ class TorusCable(object):
# print(theta, end=" ") # print(theta, end=" ")
# print(sum) # print(sum)
if sum.is_integer(): if sum.is_integer():
print("#" * 100) # print("#" * 100)
print(theta) # print(theta)
return True return True
return False return False
# if self.is_value_for_vector_class_big(vector, sigma_or_sign): # if self.is_value_for_vector_class_big(vector, sigma_or_sign):

193
main.sage
View File

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