marchwicka/signature_function
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before deleting unused fragments

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Maria Marchwicka 2019-04-07 19:46:30 +02:00
parent 259764e414
commit 6ff1b83a17
1 changed files with 79 additions and 66 deletions
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145
my_signature.sage
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@ -1,19 +1,19 @@
#!/usr/bin/env python #!/usr/bin/env python
import collections import collections
import sys import sys
def mod_one(n): def mod_one(n):
"""This function returns the fractional part of some number.""" """This function returns the fractional part of some number."""
if n >= 1: n -= int(n)
return mod_one(n - 1)
if n < 0: if n < 0:
return mod_one(n + 1) n += 1
return n return n
class av_signature_function(object): class av_signature_function(object):
''' """
This simple class encodes twisted and untwisted signature functions This simple class encodes twisted and untwisted signature functions
of knots. Since the signature function is entirely encoded by its signature of knots. Since the signature function is entirely encoded by its signature
jump, the class stores only information about signature jumps jump, the class stores only information about signature jumps
@ -22,7 +22,7 @@ class av_signature_function(object):
where the key is the argument at which the functions jumps where the key is the argument at which the functions jumps
and value encodes the value of the jump. Remember that we treat and value encodes the value of the jump. Remember that we treat
signature functions as defined on the interval [0,1). signature functions as defined on the interval [0,1).
''' """
def __init__(self, values=[]): def __init__(self, values=[]):
# We will store data of signature jumps here. # We will store data of signature jumps here.
self.data = collections.defaultdict(int) self.data = collections.defaultdict(int)
@ -46,22 +46,17 @@ class av_signature_function(object):
val += jump val += jump
return val return val
def total_sign_jump(self): def sum_of_values(self):
# Total signature jump is the sum of all jumps. # Total signature jump is the sum of all jumps.
a = sum([j[1] for j in self.to_list()]) a = sum([j[1] for j in self.to_list()])
b = sum(self.data.values()) b = sum(self.data.values())
# print b # print b
assert a == b assert a == b
assert a == 0
return sum(self.data.values()) return sum(self.data.values())
def total_absolute_sign_jump(self): def sum_of_absolute_values(self):
# Total signature jump is the sum of all jumps. return sum([abs(i) for i in self.data.values()])
a = sum([abs(j[1]) for j in self.to_list()])
# b = sum(self.data.values())
# print b
# assert a == b
return a
def double_cover(self): def double_cover(self):
new_data = [] new_data = []
@ -80,7 +75,7 @@ class av_signature_function(object):
# by the plot function. # by the plot function.
l = self.to_list() l = self.to_list()
vals = ([(d[0], sum(2 * j[1] for j in l[:l.index(d)+1])) for d in l] + vals = ([(d[0], sum(2 * j[1] for j in l[:l.index(d)+1])) for d in l] +
[(0, self.data[0]), (1, self.total_sign_jump())]) [(0, self.data[0]), (1, self.sum_of_values())])
return vals return vals
def plot(self): def plot(self):
@ -172,17 +167,12 @@ def get_twisted_signature_function(k_n, theta):
# print "normal" # print "normal"
for e in range(1, theta): for e in range(1, theta):
if (theta + e) % 2 == 0: if (theta + e) % 2 == 0:
# print e * ksi, ": 1"
# print 1 - e * ksi, ": -1 "
results.append((e * ksi, 1 * sgn(k_n))) results.append((e * ksi, 1 * sgn(k_n)))
results.append((1 - e * ksi, -1 * sgn(k_n))) results.append((1 - e * ksi, -1 * sgn(k_n)))
# print "reversed" # print "reversed"
for e in range(theta + 1, k + 1): for e in range(theta + 1, k + 1):
if (theta + e) % 2 != 0: if (theta + e) % 2 != 0:
continue continue
# print e * ksi, ": -1"
# print 1 - e * ksi, ": 1 "
results.append((e * ksi, -1 * sgn(k_n))) results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n))) results.append((1 - e * ksi, 1 * sgn(k_n)))
return av_signature_function(results) return av_signature_function(results)
@ -204,9 +194,6 @@ def get_sigma_set(p, q):
# Bl_theta(K'_(2, d) = Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t) + Bl(K')(ksi_l^theta * t) # Bl_theta(K'_(2, d) = Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t) + Bl(K')(ksi_l^theta * t)
def get_cable_signature_as_theta_function(*arg): def get_cable_signature_as_theta_function(*arg):
if len(arg) < 2:
print "It is not a cable"
return None
def signture_function(theta): def signture_function(theta):
if theta > abs(arg[-1]): if theta > abs(arg[-1]):
print "k for pattern is " + str(arg[-1]) print "k for pattern is " + str(arg[-1])
@ -233,8 +220,6 @@ def get_cable_signature_as_theta_function(*arg):
return cable_signature return cable_signature
return signture_function return signture_function
def get_untwisted_signutere_function(*arg): def get_untwisted_signutere_function(*arg):
signture_function = av_signature_function([(0, 0)]) signture_function = av_signature_function([(0, 0)])
for k_i in arg: for k_i in arg:
@ -256,6 +241,73 @@ def get_function_of_theta_for_sum(*arg):
return signature_function return signature_function
return signture_function_for_sum return signture_function_for_sum
def first_sum(k_0, k_1, k_2, k_3):
F = get_function_of_theta_for_sum([k_3, -k_2], [-k_0, -k_1, -k_3], [k_0, k_1, k_2])
for theta_0 in range(k_3 + 1):
for theta_1 in range(k_2 + 1):
f = F(theta_0, theta_1)
f.sum_of_values()
if f.sum_of_absolute_values() != 0 and theta_1 + theta_0 == 0:
print 4 * "\n"
print "OJOJOJOJJOOJJOJJ!!!!!!!!!!"
print k_0, k_1, k_2, k_3
print theta_0, theta_1
if f.sum_of_absolute_values() == 0 and theta_1 + theta_0 != 0:
# print "HURA"
# print k_0, k_1, k_2, k_3
# print theta_0, theta_1
if k_2 != k_3 or theta_0 != theta_1:
print 4 * "\n"
print " SUPER!!!!!!!!!!"
print k_0, k_1, k_2, k_3
print theta_0, theta_1
def second_sum(k_0, k_1, k_2, k_3, k_4):
F = get_function_of_theta_for_sum([], [k_0, k_1, k_2], [k_3, k_4], [-k_0, -k_3, -k_4], [-k_1, -k_2])
for theta_0 in range(k_2 + 1):
for theta_1 in range(k_4 + 1):
for theta_2 in range(k_4 + 1):
for theta_3 in range(k_2 + 1):
f = F(theta_0, theta_1, theta_2, theta_3)
if f.sum_of_absolute_values() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
print 4 * "\n"
print "2 OJOJOJOJJOOJJOJJ!!!!!!!!!!"
print k_0, k_1, k_2, k_3, k_4
print theta_0, theta_1, theta_2, theta_3
if f.sum_of_absolute_values() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
# print "HURA"
# print k_0, k_1, k_2, k_3
# print theta_0, theta_1
if k_2 != k_3 or theta_0 != theta_1:
print 4 * "\n"
print "2 SUPER!!!!!!!!!!"
print k_0, k_1, k_2, k_3, k_4
print theta_0, theta_1, theta_2, theta_3
def third_sum(k_0, k_1, k_2, k_3, k_4, k_5, k_6, k_7, k_8):
F = get_function_of_theta_for_sum([], [k_0, k_1, k_2], [k_3, k_4], [-k_5, -k_6, -k_7], [-k_8, -k_8])
for theta_0 in range(k_2 + 1):
for theta_1 in range(k_4 + 1):
for theta_2 in range(k_4 + 1):
for theta_3 in range(k_2 + 1):
f = F(theta_0, theta_1, theta_2, theta_3)
if f.sum_of_absolute_values() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
print 4 * "\n"
print "3 OJOJOJOJJOOJJOJJ!!!!!!!!!!"
print k_0, k_1, k_2, k_3, k_4
print theta_0, theta_1, theta_2, theta_3
if f.sum_of_absolute_values() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
# print "HURA"
# print k_0, k_1, k_2, k_3
# print theta_0, theta_1
if k_2 != k_3 or theta_0 != theta_1:
print 4 * "\n"
print "3 SUPER!!!!!!!!!!"
print k_0, k_1, k_2, k_3, k_4
print theta_0, theta_1, theta_2, theta_3
def tmp(limit=None): def tmp(limit=None):
if limit is None: if limit is None:
@ -264,45 +316,6 @@ def tmp(limit=None):
for k_1 in range(1, limit): for k_1 in range(1, limit):
for k_2 in range(1, limit): for k_2 in range(1, limit):
for k_3 in range(1, limit): for k_3 in range(1, limit):
F = get_function_of_theta_for_sum([k_3, -k_2], [-k_0, -k_1, -k_3], [k_0, k_1, k_2]) first_sum(k_0, k_1, k_2, k_3)
for theta_0 in range(k_3 + 1):
for theta_1 in range(k_2 + 1):
f = F(theta_0, theta_1)
if f.total_absolute_sign_jump() != 0 and theta_1 + theta_0 == 0:
print 4 * "\n"
print "OJOJOJOJJOOJJOJJ!!!!!!!!!!"
print k_0, k_1, k_2, k_3
print theta_0, theta_1
if f.total_absolute_sign_jump() == 0 and theta_1 + theta_0 != 0:
# print "HURA"
# print k_0, k_1, k_2, k_3
# print theta_0, theta_1
if k_2 != k_3 or theta_0 != theta_1:
print 4 * "\n"
print " SUPER!!!!!!!!!!"
print k_0, k_1, k_2, k_3
print theta_0, theta_1
for k_4 in range(1, limit): for k_4 in range(1, limit):
F = get_function_of_theta_for_sum([], [k_0, k_1, k_2], [k_3, k_4], [-k_0, -k_3, -k_4], [-k_1, -k_2]) second_sum(k_0, k_1, k_2, k_3, k_4)
for theta_0 in range(k_2 + 1):
for theta_1 in range(k_4 + 1):
for theta_2 in range(k_4 + 1):
for theta_3 in range(k_2 + 1):
f = F(theta_0, theta_1, theta_2, theta_3)
if f.total_absolute_sign_jump() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
print 4 * "\n"
print "2 OJOJOJOJJOOJJOJJ!!!!!!!!!!"
print k_0, k_1, k_2, k_3, k_4
print theta_0, theta_1, theta_2, theta_3
if f.total_absolute_sign_jump() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
# print "HURA"
# print k_0, k_1, k_2, k_3
# print theta_0, theta_1
if k_2 != k_3 or theta_0 != theta_1:
print 4 * "\n"
print "2 SUPER!!!!!!!!!!"
print k_0, k_1, k_2, k_3, k_4
print theta_0, theta_1, theta_2, theta_3