some bad comments

This commit is contained in:
Maria Marchwicka 2020-07-13 21:03:26 +02:00
parent c168b16d73
commit 2477c79297

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@ -1,5 +1,6 @@
#!/usr/bin/python
# TBD: read about Factory Method, variable in docstring, sage documentation
def calculate_form(x, y, q4):
x1, x2, x3, x4 = x
y1, y2, y3, y4 = y
@ -8,8 +9,7 @@ def calculate_form(x, y, q4):
return form
def check_condition(v, q4):
form = calculate_form(v, v, q4)
if form:
if calculate_form(v, v, q4):
return False
return True
@ -91,8 +91,8 @@ class MySettings(object):
"""
About notation:
Cables that we work with follow a schema:
T(2, q_0; 2, q_1; 2, q_2) # T(2, q_1; 2, q_2) #
# -T(2, q_3; 2, q_2) # -T(2, q_0; 2, q_3; 2, q_2)
T(2, q_0; 2, q_1; 2, q_2) # T(2, q_1; 2, q_2) #
# -T(2, q_3; 2, q_2) # -T(2, q_0; 2, q_3; 2, q_2)
In knot_sum_formula each k[i] is related with some q_i value, where
q_i = 2*k[i] + 1.
So we can work in the following steps:
@ -280,24 +280,32 @@ def get_shifted_combination(combination):
def get_blanchfield_for_pattern(k_n, theta):
"""
This function calculates a twisted signature function for a given cable
and theta/character. It returns object of class SignatureFunction.
It is based on Proposition 9.8. in Twisted Blanchfield Pairing.
Arguments:
k_n: a number s.t. q_n = 2 * k_n + 1, where
T(2, q_n) is a pattern knot for a single cable from a cable sum
theta: twist/character for the cable (value form v vector)
Return:
SignatureFunction created for twisted signature function
for a given cable and theta/character
Based on:
Proposition 9.8. in Twisted Blanchfield Pairing
(https://arxiv.org/pdf/1809.08791.pdf)
"""
# TBD: k_n explanation
if theta == 0:
a = get_untwisted_signature_function(k_n)
return a.square_root() + a.minus_square_root()
results = []
k = abs(k_n)
ksi = 1/(2 * k + 1)
# lambda_odd (theta + e) % 2 == 0:
# 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)))
# lambda_even
# print "normal"
for e in range(1, theta):
@ -315,11 +323,14 @@ def get_blanchfield_for_pattern(k_n, theta):
def get_cable_signature_as_theta_function(*arg):
"""
This function takes as an argument a single cable T_(2, q), i.e.
arbitrary number of integers that encode the cable,
and returns another function that alow to calculate signature function
for this single cable and a theta given as an argument.
Argument:
n integers that encode a single cable, i.e.
values of q_i for T(2,q_0; 2,q_1; ... 2, q_n)
Return:
a function that returns SignatureFunction for this single cable
and a theta given as an argument
"""
def get_signture_function(theta):
"""
This function returns SignatureFunction for previously defined single
@ -328,9 +339,9 @@ def get_cable_signature_as_theta_function(*arg):
get_cable_signature_as_theta_function(*arg)
with the cable description as an argument.
It is an implementaion of the formula:
Bl_theta(K'_(2, d)) =
Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t)
+ Bl(K')(ksi_l^theta * t)
Bl_theta(K'_(2, d)) =
Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t)
+ Bl(K')(ksi_l^theta * t)
"""
# TBD: another formula (for t^2) description
@ -340,7 +351,11 @@ def get_cable_signature_as_theta_function(*arg):
msg = "k for the pattern in the cable is " + str(arg[-1]) + \
". Parameter theta should not be larger than abs(k)."
raise ValueError(msg)
# twisted part
cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
# untwisted part
for i, k in enumerate(arg[:-1][::-1]):
ksi = 1/(2 * k_n + 1)
power = 2^i
@ -422,9 +437,11 @@ def get_function_of_theta_for_sum(*arg):
def signature_function_for_sum(*thetas, **kwargs):
"""
Arguments:
Returns object of SignatureFunction class for a previously defined
connected sum of len(arg) cables.
Accept len(arg) arguments: for each cable one theta parameter.
Acept len(arg) arguments: for each cable one theta parameter.
If call with no arguments, all theta parameters are set to be 0.
"""
if 'verbose' in kwargs:
@ -534,20 +551,19 @@ def check_squares(a, k):
else:
print "Trivial " + str(knot_sum)
return None
eval_cable_for_thetas(knot_sum)
def get_number_of_combinations(*arg):
"""
Arguments:
arbitrary number of lists of numbers, each list encodes a single cable.
arbitrary number of lists of numbers, each list encodes a single cable
Return:
number of possible theta values combinations that could be applied
for a given cable sum,
i.e. the product of q_j for j = {1,.. n},
where n is a number of direct components in the cable sum,
and q_j is the last q parameter for the component (a single cable).
and q_j is the last q parameter for the component (a single cable)
"""
number_of_combinations = 1
for knot in arg:
@ -575,7 +591,7 @@ def mod_one(n):
Argument:
a number
Return:
the fractional part of a number
the fractional part of the argument
Examples:
sage: mod_one(9 + 3/4)
3/4