marchwicka/signature_function
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after fixing bag with dictionary in init of SignatureFunction

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Maria Marchwicka 2020-09-15 01:52:34 +02:00
parent 8de3742c8d
commit b729a4eeee
2 changed files with 99 additions and 67 deletions
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157
cable_signature.sage
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@ -14,11 +14,16 @@ class SignatureFunction(object):
def __init__(self, values=None, counter=None):
# set values of signature jumps
if counter is None:
counter = collections.Counter()
if values is None:
values = []
assert all(x < 1 for x, y in values),\
"Signature function is defined on the interval [0, 1)."
counter = collections.Counter(dict(values))
msg = "Signature function is defined on the interval [0, 1)."
assert all(k < 1 for k, v in values), msg
for k, v in values:
counter[k] += v
self.cnt_signature_jumps = counter
def sum_of_absolute_values(self):
@ -31,6 +36,7 @@ class SignatureFunction(object):
# to read values for t^2
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump != 0:
new_data.append((jump_arg/2, jump))
new_data.append((1/2 + jump_arg/2, jump))
return SignatureFunction(values=new_data)
@ -39,7 +45,7 @@ class SignatureFunction(object):
# to read values for t^(1/2)
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg < 1/2:
if jump_arg < 1/2 and jump != 0:
new_data.append((2 * jump_arg, jump))
return SignatureFunction(values=new_data)
@ -47,16 +53,22 @@ class SignatureFunction(object):
# to read values for t^(1/2)
counter = collections.Counter()
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg >= 1/2:
if jump_arg >= 1/2 and jump != 0:
counter[mod_one(2 * jump_arg)] = jump
return SignatureFunction(counter=counter)
def is_big(self):
max = 0
items = self.cnt_signature_jumps.items()
for arg, _ in items:
# current = sum([jump for jump_arg, jump in items if jump_arg <= arg])
current = self(arg)
current = 0
items = sorted(self.cnt_signature_jumps.items())
for arg, jump in items:
current += 2 * jump
msg = "current = " + str(current) + ", jump = " + str(jump)
msg += "\n" + str(self(arg))
result = [jump for jump_arg, jump in self.cnt_signature_jumps.items() if jump_arg < mod_one(arg)]
msg += "\nresult = " + str(sum(result))
msg += "\narg = " + str(arg)
assert current == self(arg) + jump, msg
if abs(current) > abs(max):
max = current
# if abs(max) > 9:
@ -68,7 +80,12 @@ class SignatureFunction(object):
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
new_data.append((mod_one(jump_arg + shift), jump))
return SignatureFunction(values=new_data)
sf = SignatureFunction(values=new_data)
counter = collections.Counter({mod_one(k + shift) : v \
for k,v in self.cnt_signature_jumps.items()})
assert SignatureFunction(counter=counter) == \
SignatureFunction(values=new_data)
return SignatureFunction(counter=counter)
def __lshift__(self, shift):
return self.__rshift__(-shift)
@ -93,7 +110,8 @@ class SignatureFunction(object):
def __str__(self):
result = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
for jump_arg, jump in sorted(self.cnt_signature_jumps.items())])
for jump_arg, jump in sorted(self.cnt_signature_jumps.items())
if jump != 0])
return result
def __repr__(self):
@ -104,10 +122,9 @@ class SignatureFunction(object):
def __call__(self, arg):
# return the value of the signature function at the point arg, i.e.
# sum of all signature jumps that occur before arg
arg = mod_one(arg)
cnt = self.cnt_signature_jumps
before_arg = [jump for jump_arg, jump in cnt.items() if jump_arg < arg]
return 2 * sum(before_arg) + cnt[arg]
items = self.cnt_signature_jumps.items()
result = [jump for jump_arg, jump in items if jump_arg < mod_one(arg)]
return 2 * sum(result) + self.cnt_signature_jumps[arg]
def total_sign_jump(self):
# Total signature jump is the sum of all jumps.
@ -267,6 +284,65 @@ class TorusCable(object):
signature_as_function_of_theta_docstring
return signature_as_function_of_theta
@staticmethod
def get_blanchfield_for_pattern(k_n, theta):
if theta == 0:
sf = TorusCable.get_untwisted_signature_function(k_n)
return sf.square_root() + sf.minus_square_root()
results = []
k = abs(k_n)
ksi = 1/(2 * k + 1)
counter = collections.Counter()
# print("lambda_odd, i.e. (theta + e) % 2 != 0")
for e in range(1, k + 1):
if (theta + e) % 2 != 0:
counter[e * ksi] = 1 * sgn(k_n)
counter[1 - e * ksi] = -1 * sgn(k_n)
results.append((e * ksi, 1 * sgn(k_n)))
results.append((1 - e * ksi, -1 * sgn(k_n)))
# for example for k = 9 (q = 19) from this part we get
# for even theta
# 2/19: 1
# 4/19: 1
# 6/19: 1
# 8/19: 1
# 11/19: -1
# 13/19: -1
# 15/19: -1
# 17/19: -1
#
# for odd theta
# 1/19: 1
# 3/19: 1
# 5/19: 1
# 7/19: 1
# 9/19: 1
# 10/19: -1
# 12/19: -1
# 14/19: -1
# 16/19: -1
# 18/19: -1
# print("lambda_even")
# print("normal")
for e in range(1, theta):
if (theta + e) % 2 == 0:
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:
results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n)))
return SignatureFunction(values=results)
@staticmethod
def get_untwisted_signature_function(j):
# return the signature function of the T_{2,2k+1} torus knot
@ -277,6 +353,7 @@ class TorusCable(object):
for a in range(k + 1, 2 * k + 1)])
return SignatureFunction(values=w)
def get_knot_descrption(self):
description = ""
for knot in self.knot_sum:
@ -327,56 +404,6 @@ class TorusCable(object):
get_summand_signture_function_docsting
return get_summand_signture_function
def get_blanchfield_for_pattern(self, k_n, theta):
if theta == 0:
sf = TorusCable.get_untwisted_signature_function(k_n)
return sf.square_root() + sf.minus_square_root()
results = []
k = abs(k_n)
ksi = 1/(2 * k + 1)
# print("lambda_odd, i.e. (theta + e) % 2 != 0")
for e in range(1, k + 1):
if (theta + e) % 2 != 0:
results.append((e * ksi, 1 * sgn(k_n)))
results.append((1 - e * ksi, -1 * sgn(k_n)))
# for example for k = 9 (q = 19) from this part we get
# for even theta
# 2/19: 1
# 4/19: 1
# 6/19: 1
# 8/19: 1
# 11/19: -1
# 13/19: -1
# 15/19: -1
# 17/19: -1
#
# for odd theta
# 1/19: 1
# 3/19: 1
# 5/19: 1
# 7/19: 1
# 9/19: 1
# 10/19: -1
# 12/19: -1
# 14/19: -1
# 16/19: -1
# 18/19: -1
# print("lambda_even")
# print("normal")
for e in range(1, theta):
if (theta + e) % 2 == 0:
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:
results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n)))
return SignatureFunction(values=results)
def get_number_of_combinations_of_theta(self):
number_of_combinations = 1

5
my_signature.sage
View File

@ -23,6 +23,10 @@ class Config(object):
self.knot_formula = "[[k[0], k[1], k[3]], [-k[1], -k[3]], \
[k[2], k[3]], [-k[0], -k[2], -k[3]]]"
# self.knot_formula = "[[k[3]], [-k[3]], \
# [k[3]], [-k[3]] ]"
# self.knot_formula = "[[k[3], k[2], k[0]], [-k[2], -k[0]], \
# [k[1], k[0]], [-k[3], -k[1], -k[0]]]"
@ -198,6 +202,7 @@ def search_for_large_signature_value(knot_formula=None, limit=None,
# iterate over q-vector
for c in combinations:
q = [P.unrank(i + config.start_shift) for i in c]
q[3] = 79
if config.only_slice_candidates:
if not (q[3] > 4 * q[2] and
q[2] > 4 * q[1] and