before deleting unused fragments

This commit is contained in:
Maria Marchwicka 2019-04-07 19:46:30 +02:00
parent 259764e414
commit 6ff1b83a17

View File

@ -1,19 +1,19 @@
#!/usr/bin/env python
import collections
import sys
def mod_one(n):
"""This function returns the fractional part of some number."""
if n >= 1:
return mod_one(n - 1)
n -= int(n)
if n < 0:
return mod_one(n + 1)
n += 1
return n
class av_signature_function(object):
'''
"""
This simple class encodes twisted and untwisted signature functions
of knots. Since the signature function is entirely encoded by its signature
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
and value encodes the value of the jump. Remember that we treat
signature functions as defined on the interval [0,1).
'''
"""
def __init__(self, values=[]):
# We will store data of signature jumps here.
self.data = collections.defaultdict(int)
@ -46,22 +46,17 @@ class av_signature_function(object):
val += jump
return val
def total_sign_jump(self):
def sum_of_values(self):
# Total signature jump is the sum of all jumps.
a = sum([j[1] for j in self.to_list()])
b = sum(self.data.values())
# print b
assert a == b
assert a == 0
return sum(self.data.values())
def total_absolute_sign_jump(self):
# Total signature jump is the sum of all jumps.
a = sum([abs(j[1]) for j in self.to_list()])
# b = sum(self.data.values())
# print b
# assert a == b
return a
def sum_of_absolute_values(self):
return sum([abs(i) for i in self.data.values()])
def double_cover(self):
new_data = []
@ -80,7 +75,7 @@ class av_signature_function(object):
# by the plot function.
l = self.to_list()
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
def plot(self):
@ -172,17 +167,12 @@ def get_twisted_signature_function(k_n, theta):
# print "normal"
for e in range(1, theta):
if (theta + e) % 2 == 0:
# print e * ksi, ": 1"
# print 1 - e * ksi, ": -1 "
results.append((e * ksi, 1 * sgn(k_n)))
results.append((1 - e * ksi, -1 * sgn(k_n)))
# print "reversed"
for e in range(theta + 1, k + 1):
if (theta + e) % 2 != 0:
continue
# print e * ksi, ": -1"
# print 1 - e * ksi, ": 1 "
results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n)))
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)
def get_cable_signature_as_theta_function(*arg):
if len(arg) < 2:
print "It is not a cable"
return None
def signture_function(theta):
if theta > abs(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 signture_function
def get_untwisted_signutere_function(*arg):
signture_function = av_signature_function([(0, 0)])
for k_i in arg:
@ -256,25 +241,19 @@ def get_function_of_theta_for_sum(*arg):
return signature_function
return signture_function_for_sum
def tmp(limit=None):
if limit is None:
limit = 10
for k_0 in range(1, limit):
for k_1 in range(1, limit):
for k_2 in range(1, limit):
for k_3 in range(1, limit):
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)
if f.total_absolute_sign_jump() != 0 and theta_1 + theta_0 == 0:
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.total_absolute_sign_jump() == 0 and theta_1 + theta_0 != 0:
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
@ -284,20 +263,20 @@ def tmp(limit=None):
print k_0, k_1, k_2, k_3
print theta_0, theta_1
for k_4 in range(1, limit):
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.total_absolute_sign_jump() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
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.total_absolute_sign_jump() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
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
@ -306,3 +285,37 @@ def tmp(limit=None):
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):
if limit is None:
limit = 10
for k_0 in range(1, limit):
for k_1 in range(1, limit):
for k_2 in range(1, limit):
for k_3 in range(1, limit):
first_sum(k_0, k_1, k_2, k_3)
for k_4 in range(1, limit):
second_sum(k_0, k_1, k_2, k_3, k_4)