counting for special cases
This commit is contained in:
Maria Marchwicka
parent
7b3f3f8a23
commit
259764e414
@ -1,5 +1,6 @@
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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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@ -29,9 +30,9 @@ class av_signature_function(object):
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for jump_arg, jump in values:
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assert 0 <= jump_arg < 1, \
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"Signature function is defined on the interval [0, 1)."
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################################### what for += ???
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self.data[jump_arg] = jump
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def value(self, arg):
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# Compute the value of the signature function at the point arg.
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# This requires summing all signature jumps that occur before arg.
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@ -45,7 +46,6 @@ class av_signature_function(object):
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val += jump
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return val
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############## what for - it is == 0
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def total_sign_jump(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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@ -54,6 +54,23 @@ class av_signature_function(object):
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assert a == b
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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 double_cover(self):
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new_data = []
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for jump_arg, jump in self.data.items():
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new_data.append((mod_one(jump_arg/2), jump))
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new_data.append((mod_one(1/2 + jump_arg/2), jump))
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return av_signature_function(new_data)
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def to_list(self):
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# Return signature jumps formated as a list
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return sorted(self.data.items(), key=lambda x: x[0])
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@ -115,22 +132,177 @@ class av_signature_function(object):
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return self
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def __add__(self, other):
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new_one = av_signature_function()
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new_data = collections.defaultdict(int)
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for jump_arg, jump in other.data.items():
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self.data[jump_arg] += jump
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return self
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new_data[jump_arg] = jump + self.data.get(jump_arg, 0)
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try:
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int(jump_arg)
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except:
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print jump_arg
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for jump_arg, jump in self.data.items():
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if jump_arg not in new_data.keys():
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new_data[jump_arg] = self.data[jump_arg]
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new_one.data = new_data
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return new_one
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def __str__(self):
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return '\n'.join([str(jump_arg) + ": " + str(jump)
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for jump_arg, jump in self.data.items()])
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for jump_arg, jump in sorted(self.data.items())])
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def __repr__(self):
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return self.__str__()
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# 9.8
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# ksi = exp( (2 PI * i) / (2k + 1))
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# blanchfield = lambda_even + lambda_odd
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def untw_signature(k):
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# Return the signature function of the T_{2,2k+1} torus knot.
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l = ([((2 * a + 1)/(4 * k + 2), -1) for a in range(k)] +
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[((2 * a + 1)/(4 * k + 2), 1) for a in range(k + 1, 2 * k + 1)])
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# print l
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# print type(l)
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return av_signature_function(l)
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def get_twisted_signature_function(k_n, theta):
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results = []
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k = abs(k_n)
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ksi = 1/(2 * k + 1)
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# lambda_odd (theta + e) % 2 == 0:
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for e in range(1, k + 1):
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if (theta + e) % 2 != 0:
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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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# lambda_even
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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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def get_blanchfield(t, k):
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p = 2
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q = 2 * k + 1
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sigma_set = get_sigma_set(p, q)
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sigma = len(sigma_set) - 2 * len([z for z in sigma_set if t < z < 1 + t])
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return sigma
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def get_sigma_set(p, q):
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sigma_set = set()
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for i in range(1, p):
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for j in range(1, q):
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sigma_set.add(j/q + i/p)
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return sigma_set
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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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print "theta shouldn't be larger than this"
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return None
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if theta == 0:
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cable_signature = get_untwisted_signutere_function(arg[-1])
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else:
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cable_signature = get_twisted_signature_function(arg[-1], theta)
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for i, k_i in enumerate(arg[:-1][::-1]):
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k = abs(k_i)
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ksi = 1/(2 * k + 1)
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power = 2^i
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a = get_untwisted_signutere_function(k_i)
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shift = theta * ksi * power
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b = a >> shift
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c = a << shift
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for _ in range(i):
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b = b.double_cover()
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c = c.double_cover()
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b += c
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cable_signature += b
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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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k = abs(k_i)
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# Return the signature function of the T_{2,2k+1} torus knot.
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l = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(k_i)) for a in range(k)] +
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[((2 * a + 1)/(4 * k + 2), 1 * sgn(k_i)) for a in range(k + 1, 2 * k + 1)])
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signture_function += av_signature_function(l)
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return signture_function
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def get_function_of_theta_for_sum(*arg):
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def signture_function_for_sum(*thetas):
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if len(thetas) != len(arg) - 1:
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print "For each cable one theta value should be given"
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return None
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signature_function = get_untwisted_signutere_function(*arg[0])
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for i, knot in enumerate(arg[1:]):
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signature_function += (get_cable_signature_as_theta_function(*knot))(thetas[i])
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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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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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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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# 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 " SUPER!!!!!!!!!!"
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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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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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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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# 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 "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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