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get_sign_jump function

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Maria Marchwicka 2020-05-26 17:23:47 +02:00
parent ff8285e952
commit e815de8846
1 changed files with 20 additions and 10 deletions
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my_signature.sage
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@ -1,15 +1,16 @@
#!/usr/bin/env python #!/usr/bin/python
# TBD: remove part of the description to readme/example # TBD: remove part of the description to readme/example
""" """
This script calculates signature functions for knots (cable sums). This script calculates signature functions for knots (cable sums).
The script can be run as a sage script from the terminal or used in interactive The script can be run as a sage script from the terminal or used in interactive
mode. modeselfself.
A knot (cable sum) is encoded as a list where each element (also a list)
corresponds to a cable knot.
To calculate the number of characters for which signature function vanish use To calculate the number of characters for which signature function vanish use
the function eval_cable_for_thetas as shown below: the function eval_cable_for_thetas as shown below.
sage: eval_cable_for_thetas([[1, 3], [2], [-1, -2], [-3]]) sage: eval_cable_for_thetas([[1, 3], [2], [-1, -2], [-3]])
@ -42,7 +43,7 @@ sage: print sf
13/30: -1 13/30: -1
19/42: -1 19/42: -1
23/42: 1 23/42: 1
17/30: 1 17/30: 1
4/7: 0 4/7: 0
3/5: -1 3/5: -1
23/30: 1 23/30: 1
@ -53,7 +54,7 @@ sage:
or like below: or like below:
sage: print get_function_of_theta_for_sum([1, 3], [2], [-1, -2], [-3])(2, 1, 2, 2) sage: print get_function_of_theta_for_sum([1, 3], [2], [-1, -2], [-3])(2, 1, 2, 2)
0: 0 0: 0
1/7: 0 1/7: 0
1/6: 0 1/6: 0
@ -79,6 +80,7 @@ import pandas as pd
import re import re
class MySettings(object): class MySettings(object):
def __init__(self): def __init__(self):
self.f_results = os.path.join(os.getcwd(), "results.out") self.f_results = os.path.join(os.getcwd(), "results.out")
@ -137,6 +139,9 @@ class SignatureFunction(object):
new_data.append((2 * jump_arg, jump)) new_data.append((2 * jump_arg, jump))
return SignatureFunction(new_data) return SignatureFunction(new_data)
def get_signture_jump(self, t):
return self.data.get(t, 0)
def minus_square_root(self): def minus_square_root(self):
# to read values for t^(1/2) # to read values for t^(1/2)
@ -326,9 +331,9 @@ def get_cable_signature_as_theta_function(*arg):
k_n = abs(arg[-1]) k_n = abs(arg[-1])
if theta > k_n: if theta > k_n:
print "k for the pattern in the cable is " + str(arg[-1]) msg = "k for the pattern in the cable is " + str(arg[-1]) + \
print "theta shouldn't be larger than this" ". Parameter theta should not be larger than abs(k)."
return None raise ValueError(msg)
cable_signature = get_blanchfield_for_pattern(arg[-1], theta) cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
for i, k in enumerate(arg[:-1][::-1]): for i, k in enumerate(arg[:-1][::-1]):
ksi = 1/(2 * k_n + 1) ksi = 1/(2 * k_n + 1)
@ -390,7 +395,12 @@ def get_function_of_theta_for_sum(*arg):
raise TypeError(msg) raise TypeError(msg)
sf = SignatureFunction([(0, 0)]) sf = SignatureFunction([(0, 0)])
for i, knot in enumerate(arg): for i, knot in enumerate(arg):
sf += (get_cable_signature_as_theta_function(*knot))(thetas[i]) try:
sf += (get_cable_signature_as_theta_function(*knot))(thetas[i])
except ValueError as e:
print "ValueError: " + str(e.args[0]) +\
" Please change " + str(i + 1) + ". parameter."
return None
if verbose: if verbose:
print print
print str(*thetas) print str(*thetas)