before deleting unused fragments
This commit is contained in:
Maria Marchwicka
parent
259764e414
commit
6ff1b83a17
@ -1,19 +1,19 @@
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#!/usr/bin/env python
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import collections
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import sys
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def mod_one(n):
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"""This function returns the fractional part of some number."""
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if n >= 1:
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return mod_one(n - 1)
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n -= int(n)
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if n < 0:
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return mod_one(n + 1)
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n += 1
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return n
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class av_signature_function(object):
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'''
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"""
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This simple class encodes twisted and untwisted signature functions
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of knots. Since the signature function is entirely encoded by its signature
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jump, the class stores only information about signature jumps
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@ -22,7 +22,7 @@ class av_signature_function(object):
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where the key is the argument at which the functions jumps
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and value encodes the value of the jump. Remember that we treat
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signature functions as defined on the interval [0,1).
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'''
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"""
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def __init__(self, values=[]):
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# We will store data of signature jumps here.
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self.data = collections.defaultdict(int)
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@ -46,22 +46,17 @@ class av_signature_function(object):
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val += jump
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return val
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def total_sign_jump(self):
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def sum_of_values(self):
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# Total signature jump is the sum of all jumps.
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a = sum([j[1] for j in self.to_list()])
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b = sum(self.data.values())
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# print b
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assert a == b
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assert a == 0
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return sum(self.data.values())
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def total_absolute_sign_jump(self):
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# Total signature jump is the sum of all jumps.
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a = sum([abs(j[1]) for j in self.to_list()])
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# b = sum(self.data.values())
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# print b
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# assert a == b
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return a
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def sum_of_absolute_values(self):
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return sum([abs(i) for i in self.data.values()])
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def double_cover(self):
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new_data = []
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@ -80,7 +75,7 @@ class av_signature_function(object):
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# by the plot function.
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l = self.to_list()
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vals = ([(d[0], sum(2 * j[1] for j in l[:l.index(d)+1])) for d in l] +
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[(0, self.data[0]), (1, self.total_sign_jump())])
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[(0, self.data[0]), (1, self.sum_of_values())])
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return vals
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def plot(self):
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@ -172,17 +167,12 @@ def get_twisted_signature_function(k_n, theta):
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# print "normal"
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for e in range(1, theta):
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if (theta + e) % 2 == 0:
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# print e * ksi, ": 1"
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# print 1 - e * ksi, ": -1 "
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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 "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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continue
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# print e * ksi, ": -1"
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# print 1 - e * ksi, ": 1 "
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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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return av_signature_function(results)
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@ -204,9 +194,6 @@ def get_sigma_set(p, q):
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# Bl_theta(K'_(2, d) = Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t) + Bl(K')(ksi_l^theta * t)
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def get_cable_signature_as_theta_function(*arg):
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if len(arg) < 2:
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print "It is not a cable"
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return None
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def signture_function(theta):
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if theta > abs(arg[-1]):
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print "k for pattern is " + str(arg[-1])
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@ -233,8 +220,6 @@ def get_cable_signature_as_theta_function(*arg):
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return cable_signature
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return signture_function
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def get_untwisted_signutere_function(*arg):
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signture_function = av_signature_function([(0, 0)])
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for k_i in arg:
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@ -256,25 +241,19 @@ def get_function_of_theta_for_sum(*arg):
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return signature_function
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return signture_function_for_sum
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def tmp(limit=None):
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if limit is None:
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limit = 10
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for k_0 in range(1, limit):
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for k_1 in range(1, limit):
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for k_2 in range(1, limit):
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for k_3 in range(1, limit):
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def first_sum(k_0, k_1, k_2, k_3):
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F = get_function_of_theta_for_sum([k_3, -k_2], [-k_0, -k_1, -k_3], [k_0, k_1, k_2])
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for theta_0 in range(k_3 + 1):
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for theta_1 in range(k_2 + 1):
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f = F(theta_0, theta_1)
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if f.total_absolute_sign_jump() != 0 and theta_1 + theta_0 == 0:
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f.sum_of_values()
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if f.sum_of_absolute_values() != 0 and theta_1 + theta_0 == 0:
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print 4 * "\n"
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print "OJOJOJOJJOOJJOJJ!!!!!!!!!!"
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print k_0, k_1, k_2, k_3
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print theta_0, theta_1
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if f.total_absolute_sign_jump() == 0 and theta_1 + theta_0 != 0:
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if f.sum_of_absolute_values() == 0 and theta_1 + theta_0 != 0:
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# print "HURA"
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# print k_0, k_1, k_2, k_3
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# print theta_0, theta_1
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@ -284,20 +263,20 @@ def tmp(limit=None):
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print k_0, k_1, k_2, k_3
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print theta_0, theta_1
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for k_4 in range(1, limit):
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def second_sum(k_0, k_1, k_2, k_3, k_4):
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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])
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for theta_0 in range(k_2 + 1):
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for theta_1 in range(k_4 + 1):
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for theta_2 in range(k_4 + 1):
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for theta_3 in range(k_2 + 1):
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f = F(theta_0, theta_1, theta_2, theta_3)
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if f.total_absolute_sign_jump() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
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if f.sum_of_absolute_values() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
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print 4 * "\n"
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print "2 OJOJOJOJJOOJJOJJ!!!!!!!!!!"
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print k_0, k_1, k_2, k_3, k_4
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print theta_0, theta_1, theta_2, theta_3
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if f.total_absolute_sign_jump() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
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if f.sum_of_absolute_values() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
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# print "HURA"
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# print k_0, k_1, k_2, k_3
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# print theta_0, theta_1
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@ -306,3 +285,37 @@ def tmp(limit=None):
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print "2 SUPER!!!!!!!!!!"
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print k_0, k_1, k_2, k_3, k_4
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print theta_0, theta_1, theta_2, theta_3
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def third_sum(k_0, k_1, k_2, k_3, k_4, k_5, k_6, k_7, k_8):
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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])
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for theta_0 in range(k_2 + 1):
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for theta_1 in range(k_4 + 1):
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for theta_2 in range(k_4 + 1):
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for theta_3 in range(k_2 + 1):
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f = F(theta_0, theta_1, theta_2, theta_3)
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if f.sum_of_absolute_values() != 0 and theta_1 + theta_0 + theta_3 + theta_2 == 0:
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print 4 * "\n"
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print "3 OJOJOJOJJOOJJOJJ!!!!!!!!!!"
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print k_0, k_1, k_2, k_3, k_4
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print theta_0, theta_1, theta_2, theta_3
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if f.sum_of_absolute_values() == 0 and theta_1 + theta_0 + theta_3 + theta_2 != 0:
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# print "HURA"
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# print k_0, k_1, k_2, k_3
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# print theta_0, theta_1
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if k_2 != k_3 or theta_0 != theta_1:
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print 4 * "\n"
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print "3 SUPER!!!!!!!!!!"
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print k_0, k_1, k_2, k_3, k_4
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print theta_0, theta_1, theta_2, theta_3
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def tmp(limit=None):
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if limit is None:
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limit = 10
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for k_0 in range(1, limit):
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for k_1 in range(1, limit):
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for k_2 in range(1, limit):
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for k_3 in range(1, limit):
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first_sum(k_0, k_1, k_2, k_3)
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for k_4 in range(1, limit):
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second_sum(k_0, k_1, k_2, k_3, k_4)
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