list of ranges, class Cable
This commit is contained in:
Maria Marchwicka
parent
4cdb4622ab
commit
1cc1de2e04
|
|
@ -216,22 +216,36 @@ class TorusCable(object):
|
|||
return None
|
||||
else:
|
||||
k_vector = [(q - 1)/2 for q in q_vector]
|
||||
# elif q_vector is None:
|
||||
# q_vector = [2 * k + 1 for k in k_vector]
|
||||
# self.knot_sum = eval(knot_formula)
|
||||
elif q_vector is None:
|
||||
q_vector = [2 * k + 1 for k in k_vector]
|
||||
self.knot_formula = knot_formula
|
||||
self.k_vector = k_vector
|
||||
self.q_vector = q_vector
|
||||
k = k_vector
|
||||
self.knot_sum = eval(knot_formula)
|
||||
self.knot_description = get_knot_descrption(*self.knot_sum)
|
||||
self.sigma_function = None
|
||||
|
||||
def is_sigma_for_vector_class_big(self, theta_vector):
|
||||
# check sigma for all v = s * [a_1, a_2, a_3, a_4] for s in [1, q_4 - 1]
|
||||
def __is_sigma_for_vector_class_big(self, theta_vector):
|
||||
[a_1, a_2, a_3, a_4] = theta_vector
|
||||
q_4 = self.q_vector[3]
|
||||
for shift in range(1, q_4):
|
||||
shifted_theta = [(shift * a) % q_4 for a in
|
||||
[a_1, a_2, a_3, a_4]]
|
||||
sigma_v = self.__calculate_sigma(shifted_theta)
|
||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
||||
return True
|
||||
return False
|
||||
|
||||
|
||||
def is_sigma_for_vector_class_big(self, theta_vector):
|
||||
if self.sigma_function is None:
|
||||
self.sigma_function = self.__get_sigma_function()
|
||||
return self.__is_sigma_for_vector_class_big(theta_vector)
|
||||
|
||||
|
||||
def __get_sigma_function(self):
|
||||
print("settinf the function ")
|
||||
k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
|
||||
q_4 = 2 * k_4 + 1
|
||||
ksi = 1/q_4
|
||||
|
|
@ -267,180 +281,98 @@ class TorusCable(object):
|
|||
def __calculate_sigma(self, theta_vector):
|
||||
return self.sigma_function(theta_vector)
|
||||
|
||||
# searching for sigma > 5 + #(v_i != 0)
|
||||
def check_combinations_in_range(self, range_list):
|
||||
if self.sigma_function is None:
|
||||
self.sigma_function = self.__get_sigma_function()
|
||||
large_sigma_for_all_combinations = True
|
||||
bad_vectors = []
|
||||
good_vectors = []
|
||||
q_4 = self.q_vector[-1]
|
||||
for vector in range_list:
|
||||
a_1, a_2, a_3, a_4 = vector
|
||||
if a_1 == a_2 == a_3 == a_4:
|
||||
continue
|
||||
if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
|
||||
continue
|
||||
|
||||
|
||||
if self.__is_sigma_for_vector_class_big(vector):
|
||||
good_vectors.append(vector)
|
||||
pass
|
||||
else:
|
||||
bad_vectors.append(vector)
|
||||
large_sigma_for_all_combinations = False
|
||||
return good_vectors, bad_vectors
|
||||
|
||||
|
||||
|
||||
# def is_condition_for_vector_class_fulfilled(vector):
|
||||
# a_1, a_2, a_3, a_4 = vector
|
||||
# q_4 = self.q_vector[-1]
|
||||
# # check assumption - for results != 0 mod q_4 we stop here
|
||||
# if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
|
||||
# return None
|
||||
# if self.sigma_function is None:
|
||||
# self.sigma_function = self.__get_sigma_function()
|
||||
# return self.__is_sigma_for_vector_class_big(theta_vector)
|
||||
|
||||
|
||||
# searching for sigma > 5 + #(v_i != 0)
|
||||
def eval_cable_for_large_sigma(k_vector=None, knot_formula=None,
|
||||
print_results=True, verbose=None,
|
||||
q_vector=None):
|
||||
|
||||
cable = TorusCable(knot_formula=knot_formula, k_vector=k_vector,
|
||||
q_vector=q_vector)
|
||||
# k is a k_vector
|
||||
k = cable.k_vector
|
||||
knot_description = cable.knot_description
|
||||
print("\n" * 5)
|
||||
print(knot_description)
|
||||
k_1, k_2, k_3, k_4 = [abs(i) for i in k]
|
||||
q_4 = 2 * k_4 + 1
|
||||
ksi = 1/q_4
|
||||
|
||||
q = cable.q_vector[-1]
|
||||
|
||||
if verbose:
|
||||
print("\n\n")
|
||||
print(100 * "*")
|
||||
print("Searching for a large signature values for the cable sum: ")
|
||||
print(knot_description)
|
||||
print(cable.knot_description)
|
||||
|
||||
large_sigma_for_all_v_combinations = True
|
||||
bad_vectors = []
|
||||
good_vectors = []
|
||||
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)),
|
||||
|
||||
# iteration over all possible character combinations
|
||||
# T(2, q_1; 2, q_2; 2, q_4) # -T(2, q_2; 2, q_4) #
|
||||
# # T(2, q_3; 2, q_4) # -T(2, q_1; 2, q_3; 2, q_4)
|
||||
last_theta = 1
|
||||
large_sigma_for_last_theta_non_zero = True
|
||||
for vector in it.product(range(q_4), range(q_4), range(q_4)):
|
||||
v_theta = list(vector)
|
||||
v_theta.append(last_theta)
|
||||
# a_1 == 0, a_2, a_3, a_4 != 0
|
||||
it.product(range(1), range(1, q), range(1, q), 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)),
|
||||
# a_3 == 0, a_1, a_2, a_4 != 0
|
||||
it.product(range(1, q), range(1, q), 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)),
|
||||
|
||||
a_1, a_2, a_3 = list(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
|
||||
# a_1 == 0, a_2 == 0, a_3, a_4 != 0
|
||||
it.product(range(1), range(1), range(1, q), 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)),
|
||||
# a_1 == 0, a_4 == 0, a_3, a_2 != 0
|
||||
it.product(range(1), range(1, q), 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)),
|
||||
# a_2 == 0, a_4 == 0, a_1, a_3 != 0
|
||||
it.product(range(1, q), 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)),
|
||||
|
||||
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]]
|
||||
]
|
||||
for ranges in list_of_ranges:
|
||||
good_vectors, bad_vectors = cable.check_combinations_in_range(ranges)
|
||||
|
||||
|
||||
print("good_vectors : bad_vectors: " + str(len(good_vectors)) +\
|
||||
" : " + str(len(bad_vectors)))
|
||||
#
|
||||
# print("\ngood_vectors")
|
||||
# print(len(good_vectors))
|
||||
# print("\nbad_vectors")
|
||||
# print(len(bad_vectors))
|
||||
# print(bad_vectors)
|
||||
|
||||
sigma_v = cable.calculate_sigma(shifted_theta)
|
||||
|
||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
||||
large_sigma_for_this_vector = True
|
||||
break
|
||||
|
||||
if large_sigma_for_this_vector:
|
||||
good_vectors.append(v_theta)
|
||||
pass
|
||||
else:
|
||||
bad_vectors.append(v_theta)
|
||||
large_sigma_for_last_theta_non_zero = False
|
||||
|
||||
print("\ngood_vectors")
|
||||
print(len(good_vectors))
|
||||
print("\nbad_vectors")
|
||||
print(len(bad_vectors))
|
||||
print(bad_vectors)
|
||||
bad_vectors = []
|
||||
good_vectors = []
|
||||
|
||||
large_sigma_for_last_theta_zero = True
|
||||
for vector in it.product(range(q_4), range(q_4)):
|
||||
v_theta = list(vector)
|
||||
v_theta.append(1)
|
||||
v_theta.append(0)
|
||||
a_1, a_2 = vector
|
||||
a_3 = 1
|
||||
a_4 = 0
|
||||
assert [a_1, a_2, a_3, a_4] == v_theta
|
||||
|
||||
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]]
|
||||
|
||||
sigma_v = cable.calculate_sigma(shifted_theta)
|
||||
|
||||
|
||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
||||
large_sigma_for_this_vector = True
|
||||
break
|
||||
|
||||
if large_sigma_for_this_vector:
|
||||
good_vectors.append(v_theta)
|
||||
pass
|
||||
else:
|
||||
bad_vectors.append(v_theta)
|
||||
large_sigma_for_last_theta_zero = False
|
||||
# break
|
||||
|
||||
print("\ngood_vectors")
|
||||
print(len(good_vectors))
|
||||
print("\nbad_vectors")
|
||||
print(len(bad_vectors))
|
||||
print(bad_vectors)
|
||||
bad_vectors = []
|
||||
good_vectors = []
|
||||
|
||||
print("\n\nNic nie ma")
|
||||
for vector in range(q_4):
|
||||
v_theta = [vector]
|
||||
v_theta.append(1)
|
||||
v_theta.append(0)
|
||||
v_theta.append(last_theta)
|
||||
a_1 = vector
|
||||
a_2 = 1
|
||||
a_3 = 0
|
||||
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]]
|
||||
|
||||
sigma_v = cable.calculate_sigma(shifted_theta)
|
||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
||||
large_sigma_for_this_vector = True
|
||||
break
|
||||
|
||||
if large_sigma_for_this_vector:
|
||||
good_vectors.append(v_theta)
|
||||
pass
|
||||
else:
|
||||
bad_vectors.append(v_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)
|
||||
|
||||
print("\ngood_vectors")
|
||||
print(len(good_vectors))
|
||||
print("\nbad_vectors")
|
||||
print(len(bad_vectors))
|
||||
print(bad_vectors)
|
||||
return None
|
||||
|
||||
|
||||
|
|
@ -648,11 +580,11 @@ def eval_cable_for_null_signature(knot_sum, print_results=False, verbose=None):
|
|||
null_combinations = 0
|
||||
zero_theta_combinations = []
|
||||
|
||||
ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
|
||||
range_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
|
||||
if verbose:
|
||||
print()
|
||||
print(knot_description)
|
||||
for v_theta in it.product(*ranges_list):
|
||||
for v_theta in it.product(*range_list):
|
||||
if f(*v_theta, verbose=False).is_zero_everywhere():
|
||||
zero_theta_combinations.append(v_theta)
|
||||
m = len([theta for theta in v_theta if theta != 0])
|
||||
|
|
|
|||
Loading…
Reference in New Issue