marchwicka/signature_function
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Dictionary is replaced by counter everywhere. Tests to each rpelacement.

Browse Source
This commit is contained in:
Maria Marchwicka 2020-08-05 18:23:49 +02:00
parent 9b68822357
commit 949344193c
1 changed files with 66 additions and 33 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

99
my_signature.sage
View File

@ -43,7 +43,7 @@ class Config(object):
# is the ratio restriction for values in k_vector taken into account
# False flag is usefull to make quick script tests
self.only_slice_candidates = True
# self.only_slice_candidates = False
self.only_slice_candidates = False
self.stop_after_firts_large_signature = True
self.stop_after_firts_large_signature = False
@ -60,22 +60,24 @@ class SignatureFunction(object):
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=[], counter=collections.Counter()):
def __init__(self, values=None, counter=None):
# set values of signature jumps
self.signature_jumps = collections.defaultdict(int, counter)
self.cnt_signature_jumps = counter
if not counter:
if counter is None:
counter = collections.Counter()
if values is None:
values = []
for jump_arg, jump in values:
assert 0 <= jump_arg < 1, \
"Signature function is defined on the interval [0, 1)."
self.signature_jumps[jump_arg] = jump
self.cnt_signature_jumps = collections.Counter(self.signature_jumps)
counter[jump_arg] = jump
self.cnt_signature_jumps = counter
self.signature_jumps = collections.defaultdict(int, counter)
def sum_of_absolute_values(self):
result = sum([abs(i) for i in self.signature_jumps.values()])
test = sum([abs(i) for i in self.cnt_signature_jumps.values()])
assert test == result
return result
return sum([abs(i) for i in self.cnt_signature_jumps.values()])
def is_zero_everywhere(self):
result = not any(self.signature_jumps.values())
@ -98,8 +100,8 @@ class SignatureFunction(object):
t_data.append((jump_arg/2, jump))
t_data.append((1/2 + jump_arg/2, jump))
sf = SignatureFunction(t_data)
a = SignatureFunction(new_data)
sf = SignatureFunction(values=t_data)
a = SignatureFunction(values=new_data)
assert a == sf
return sf
@ -115,24 +117,34 @@ class SignatureFunction(object):
if jump_arg < 1/2:
t_data.append((2 * jump_arg, jump))
sf = SignatureFunction(t_data)
a = SignatureFunction(new_data)
sf = SignatureFunction(values=t_data)
a = SignatureFunction(values=new_data)
assert a == sf
return sf
def minus_square_root(self):
# to read values for t^(1/2)
counter = collections.Counter()
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg >= 1/2:
counter[mod_one(2 * jump_arg)] = jump
new_data.append((mod_one(2 * jump_arg), jump))
t_data = []
for jump_arg, jump in self.signature_jumps.items():
if jump_arg >= 1/2:
t_data.append((mod_one(2 * jump_arg), jump))
a = SignatureFunction(t_data)
sf = SignatureFunction(new_data)
print(t_data)
a = SignatureFunction(values=t_data)
sf = SignatureFunction(values=new_data)
sf2 = SignatureFunction(counter=counter)
print(new_data)
print(counter.items())
assert a == sf
print("repr")
print(repr(sf2))
print(repr(a))
assert a == sf2
return sf
def __lshift__(self, shift):
@ -146,16 +158,20 @@ class SignatureFunction(object):
new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items():
new_data.append((mod_one(jump_arg + shift), jump))
sf = SignatureFunction(new_data)
a = SignatureFunction(t_data)
sf = SignatureFunction(values=new_data)
a = SignatureFunction(values=t_data)
assert a == sf
return sf
def __neg__(self):
new_data = []
print("neg")
print("start values sign and cnt")
print(self.signature_jumps.items())
print(self.cnt_signature_jumps.items())
for jump_arg, jump in self.signature_jumps.items():
new_data.append((jump_arg, -jump))
a = SignatureFunction(new_data)
a = SignatureFunction(values=new_data)
counter = collections.Counter()
counter.subtract(self.cnt_signature_jumps)
sf = SignatureFunction(counter=counter)
@ -188,33 +204,44 @@ class SignatureFunction(object):
return sf
def __str__(self):
return ''.join([str(jump_arg) + ": " + str(jump) + "\n"
result2 = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
for jump_arg, jump in sorted(self.signature_jumps.items())])
result = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
for jump_arg, jump in sorted(self.cnt_signature_jumps.items())])
assert result == result2
return result
def __repr__(self):
result = ''.join([str(jump_arg) + ": " + str(jump) + ", "
result2 = ''.join([str(jump_arg) + ": " + str(jump) + ", "
for jump_arg, jump in sorted(self.signature_jumps.items())])
result = ''.join([str(jump_arg) + ": " + str(jump) + ", "
for jump_arg, jump in sorted(self.cnt_signature_jumps.items())])
assert result == result2
return result[:-2] + "."
def __call__(self, arg):
# Compute the value of the signature function at the point arg.
# This requires summing 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]
result = 2 * sum(before_arg) + cnt[arg]
# TBD to delete
val = 0
for jump_arg, jump in self.signature_jumps.items():
if jump_arg < arg:
val += 2 * jump
elif jump_arg == arg:
val += jump
result = 0
for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg < arg:
result += 2 * jump
elif jump_arg == arg:
result += jump
assert result == val
# end of to delete
assert val == result
return val
return result
def main(arg):
@ -243,7 +270,7 @@ def search_for_large_signature_value(knot_formula=None,
limit = max(limit, k_vector_size)
combinations = it.combinations(range(1, limit + 1), k_vector_size)
P = Primes()
good_knots = []
# with open(config.f_results, 'w') as f_results:
for c in combinations:
k = [(P.unrank(i) - 1)/2 for i in c]
@ -257,6 +284,8 @@ def search_for_large_signature_value(knot_formula=None,
result = eval_cable_for_large_signature(k_vector=k,
knot_formula=knot_formula,
print_results=False)
good_knots.append(result)
return good_knots
@ -274,6 +303,9 @@ def eval_cable_for_large_signature(k_vector=None,
if q_vector is None:
# TBD docstring
print("Please give a list of k (k_vector) or q values (q_vector).")
return None
else:
k_vector = [(i - 1)/2 for i in q_vector]
k = k_vector
knot_sum = eval(knot_formula)
@ -370,7 +402,7 @@ def eval_cable_for_large_signature(k_vector=None,
print("*" * 100 + "\n" * 5)
else:
print(knot_description + "\t" + str(v_theta) +\
"\t" + str(sigma_v))
"\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
if config.stop_after_firts_large_signature:
break
else:
@ -384,7 +416,8 @@ def eval_cable_for_large_signature(k_vector=None,
print("*" * 100 + "\n" * 5)
else:
print(knot_description + "\t" + str(v_theta) +\
"\t" + str(sigma_v))
"\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
large_sigma_for_all_v_comninations = False
print("ojojojoj")
@ -634,7 +667,7 @@ def get_blanchfield_for_pattern(k_n, theta):
continue
results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n)))
return SignatureFunction(results)
return SignatureFunction(values=results)
def get_signature_summand_as_theta_function(*arg):
def get_signture_function(theta):
@ -675,7 +708,7 @@ def get_untwisted_signature_function(j):
w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
[((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
for a in range(k + 1, 2 * k + 1)])
return SignatureFunction(w)
return SignatureFunction(values=w)
def get_signature_as_theta_function(*arg, **key_args):
@ -699,7 +732,7 @@ def get_signature_as_theta_function(*arg, **key_args):
" arguments or no argument at all (" + str(lt) + " given)."
raise TypeError(msg)
sf = SignatureFunction([(0, 0)])
sf = SignatureFunction()
# for each cable in cable sum apply theta
for i, knot in enumerate(arg):