Switch to Python 3. Dictionary is replaced by counter almost everywhere. Tests to each rpelacement.
This commit is contained in:
Maria Marchwicka
parent
c7c16ab4c0
commit
9b68822357
@ -9,7 +9,6 @@ import sys
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import collections
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import inspect
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import itertools as it
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import pandas as pd
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import numpy as np
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import re
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@ -34,17 +33,17 @@ class Config(object):
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self.verbose = False
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self.print_calculations_for_small_signature = True
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# self.print_calculations_for_small_signature = False
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self.print_calculations_for_small_signature = False
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self.print_calculations_for_large_signature = True
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# self.print_calculations_for_large_signature = False
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self.print_calculations_for_large_signature = False
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# is the ratio restriction for values in k_vector taken into account
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# False flag is usefull to make quick script tests
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self.only_slice_candidates = True
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self.only_slice_candidates = False
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# self.only_slice_candidates = False
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self.stop_after_firts_large_signature = True
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self.stop_after_firts_large_signature = False
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@ -64,29 +63,45 @@ class SignatureFunction(object):
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def __init__(self, values=[], counter=collections.Counter()):
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# set values of signature jumps
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self.signature_jumps = collections.defaultdict(int, counter)
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self.counter_signature_jumps = counter
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self.cnt_signature_jumps = counter
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if not counter:
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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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self.signature_jumps[jump_arg] = jump
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self.counter_signature_jumps = collections.Counter(self.signature_jumps)
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self.cnt_signature_jumps = collections.Counter(self.signature_jumps)
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def sum_of_absolute_values(self):
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return sum([abs(i) for i in self.signature_jumps.values()])
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result = sum([abs(i) for i in self.signature_jumps.values()])
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test = sum([abs(i) for i in self.cnt_signature_jumps.values()])
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assert test == result
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return result
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def is_zero_everywhere(self):
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result = not any(self.signature_jumps.values())
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assert result == (not any(self.counter_signature_jumps.values()))
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assert result == (not any(self.cnt_signature_jumps.values()))
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if self.sum_of_absolute_values():
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assert result == False
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else:
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assert result == True
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return result
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def double_cover(self):
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# to read values for t^2
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new_data = []
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for jump_arg, jump in self.signature_jumps.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 SignatureFunction(new_data)
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new_data.append((jump_arg/2, jump))
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new_data.append((1/2 + jump_arg/2, jump))
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t_data = []
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for jump_arg, jump in self.cnt_signature_jumps.items():
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t_data.append((jump_arg/2, jump))
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t_data.append((1/2 + jump_arg/2, jump))
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sf = SignatureFunction(t_data)
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a = SignatureFunction(new_data)
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assert a == sf
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return sf
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def square_root(self):
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# to read values for t^(1/2)
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@ -94,34 +109,58 @@ class SignatureFunction(object):
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for jump_arg, jump in self.signature_jumps.items():
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if jump_arg < 1/2:
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new_data.append((2 * jump_arg, jump))
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return SignatureFunction(new_data)
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t_data = []
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for jump_arg, jump in self.cnt_signature_jumps.items():
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if jump_arg < 1/2:
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t_data.append((2 * jump_arg, jump))
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sf = SignatureFunction(t_data)
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a = SignatureFunction(new_data)
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assert a == sf
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return sf
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def minus_square_root(self):
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# to read values for t^(1/2)
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new_data = []
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for jump_arg, jump in self.signature_jumps.items():
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for jump_arg, jump in self.cnt_signature_jumps.items():
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if jump_arg >= 1/2:
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new_data.append((mod_one(2 * jump_arg), jump))
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return SignatureFunction(new_data)
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t_data = []
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for jump_arg, jump in self.signature_jumps.items():
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if jump_arg >= 1/2:
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t_data.append((mod_one(2 * jump_arg), jump))
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a = SignatureFunction(t_data)
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sf = SignatureFunction(new_data)
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assert a == sf
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return sf
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def __lshift__(self, shift):
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# A shift of the signature functions corresponds to the rotation.
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return self.__rshift__(-shift)
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def __rshift__(self, shift):
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new_data = []
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t_data = []
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for jump_arg, jump in self.signature_jumps.items():
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t_data.append((mod_one(jump_arg + shift), jump))
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new_data = []
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for jump_arg, jump in self.cnt_signature_jumps.items():
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new_data.append((mod_one(jump_arg + shift), jump))
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return SignatureFunction(new_data)
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sf = SignatureFunction(new_data)
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a = SignatureFunction(t_data)
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assert a == sf
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return sf
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def __neg__(self):
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# we can perform arithmetic operations on signature functions.
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new_data = []
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for jump_arg, jump in self.signature_jumps.items():
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new_data.append((jump_arg, -jump))
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sf = SignatureFunction(new_data)
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return SignatureFunction(new_data)
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a = SignatureFunction(new_data)
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counter = collections.Counter()
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counter.subtract(self.cnt_signature_jumps)
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sf = SignatureFunction(counter=counter)
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assert a == sf
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return sf
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# TBD short
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def __add__(self, other):
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@ -132,15 +171,21 @@ class SignatureFunction(object):
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if jump_arg not in new_data.keys():
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new_data[jump_arg] = self.signature_jumps[jump_arg]
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counter = collections.Counter()
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counter.update(self.counter_signature_jumps)
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counter.update(other.counter_signature_jumps)
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counter = copy(self.cnt_signature_jumps)
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counter.update(other.cnt_signature_jumps)
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assert collections.defaultdict(int, counter) == new_data
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return SignatureFunction(counter=counter)
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def __eq__(self, other):
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return self.cnt_signature_jumps == other.cnt_signature_jumps
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def __sub__(self, other):
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return self + other.__neg__()
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a = self + other.__neg__()
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counter = copy(self.cnt_signature_jumps)
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counter.subtract(other.cnt_signature_jumps)
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sf = SignatureFunction(counter=counter)
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assert a == sf
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return sf
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def __str__(self):
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return ''.join([str(jump_arg) + ": " + str(jump) + "\n"
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@ -154,13 +199,21 @@ class SignatureFunction(object):
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def __call__(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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assert 0 <= arg and arg < 1
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arg = mod_one(arg)
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val = 0
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for jump_arg, jump in self.signature_jumps.items():
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if jump_arg < arg:
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val += 2 * jump
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elif jump_arg == arg:
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val += jump
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result = 0
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for jump_arg, jump in self.cnt_signature_jumps.items():
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if jump_arg < arg:
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result += 2 * jump
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elif jump_arg == arg:
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result += jump
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assert val == result
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return val
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@ -199,7 +252,7 @@ def search_for_large_signature_value(knot_formula=None,
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k[2] > 4 * k[1] and
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k[1] > 4 * k[0]):
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if verbose:
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print "Ratio-condition does not hold"
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print("Ratio-condition does not hold")
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continue
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result = eval_cable_for_large_signature(k_vector=k,
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knot_formula=knot_formula,
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@ -220,7 +273,7 @@ def eval_cable_for_large_signature(k_vector=None,
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if k_vector is None:
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if q_vector is None:
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# TBD docstring
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print "Please give a list of k (k_vector) or q values (q_vector)."
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print("Please give a list of k (k_vector) or q values (q_vector).")
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k = k_vector
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knot_sum = eval(knot_formula)
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@ -231,15 +284,17 @@ def eval_cable_for_large_signature(k_vector=None,
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ksi = 1/q_4
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if verbose:
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print "\n\n"
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print 100 * "*"
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print "Searching for a large signature values for the cable sum: "
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print knot_description
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print("\n\n")
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print(100 * "*")
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print("Searching for a large signature values for the cable sum: ")
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print(knot_description)
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if len(knot_sum) != 4:
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print "Wrong number of cable direct summands!"
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print("Wrong number of cable direct summands!")
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return None
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large_sigma_for_all_v_comninations = True
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good_knots = [("nic")]
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# iteration over all possible character combinations
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ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
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for v_theta in it.product(*ranges_list):
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@ -254,9 +309,15 @@ def eval_cable_for_large_signature(k_vector=None,
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if (theta_squers[0] - theta_squers[1] +
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theta_squers[2] - theta_squers[3]) % q_4:
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if verbose:
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print "The condition is not satisfied: " + \
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str(condition) + " != 0."
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print("The condition is not satisfied: " + \
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str(condition) + " != 0.")
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continue
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if v_theta[0] == v_theta[1] == v_theta[2] == v_theta[3] == 0:
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print("\nSkip")
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continue
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if v_theta[0] == v_theta[1] == v_theta[2] == v_theta[3]:
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print("\nall v == a")
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# T(2, q_1; 2, q_2; 2, q_4) # -T(2, q_2; 2, q_4) #
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# # T(2, q_3; 2, q_4) # -T(2, q_1; 2, q_3; 2, q_4)
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@ -266,12 +327,12 @@ def eval_cable_for_large_signature(k_vector=None,
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sigma_q_2 = get_untwisted_signature_function(k_2)
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sigma_q_3 = get_untwisted_signature_function(k_3)
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a_1, a_2, a_3, a_4 = v_theta
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untwisted_part = 2 * (sigma_q_2(mod_one(ksi * a_1)) +
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sigma_q_1(mod_one(ksi * a_1 * 2)) -
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sigma_q_2(mod_one(ksi * a_2)) +
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sigma_q_3(mod_one(ksi * a_3)) -
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sigma_q_3(mod_one(ksi * a_4)) -
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sigma_q_1(mod_one(ksi * a_4 * 2)))
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untwisted_part = 2 * (sigma_q_2(ksi * a_1) +
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sigma_q_1(ksi * a_1 * 2) -
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sigma_q_2(ksi * a_2) +
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sigma_q_3(ksi * a_3) -
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sigma_q_3(ksi * a_4) -
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sigma_q_1(ksi * a_4 * 2))
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# "twisted" part
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tp = [0, 0, 0, 0]
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@ -281,48 +342,57 @@ def eval_cable_for_large_signature(k_vector=None,
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twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
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assert twisted_part == int(twisted_part)
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# y = f(*v_theta)(1/2)
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sigma_v = untwisted_part + twisted_part
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if abs(sigma_v) > 5 + np.count_nonzero(v_theta):
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if config.print_calculations_for_large_signature:
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print "*" * 100
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print "\n\nLarge signature value\n"
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print knot_description
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print "\nv_theta: ",
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print v_theta
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print "k values: ",
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print str(k_1) + " " + str(k_2) + " " + \
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str(k_3) + " " + str(k_4)
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print condition
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print "non zero value in v_theta: " + \
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str(np.count_nonzero(v_theta))
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print "sigma_v: " + str(sigma_v)
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print "\ntwisted_part: ",
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print twisted_part
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print "untwisted_part: ",
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print untwisted_part
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print "\n\nCALCULATIONS"
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print "*" * 100
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print("*" * 100)
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print("\n\nLarge signature value\n")
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print(knot_description)
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print("\nv_theta: ", end="")
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print(v_theta)
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print("k values: ", end="")
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print(str(k_1) + " " + str(k_2) + " " + \
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str(k_3) + " " + str(k_4))
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print(condition)
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print("non zero value in v_theta: " + \
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str(np.count_nonzero(v_theta)))
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print("sigma_v: " + str(sigma_v))
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print("\ntwisted_part: ", end="")
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print(twisted_part)
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print("untwisted_part: ", end="")
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print(untwisted_part)
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print("\n\nCALCULATIONS")
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print("*" * 100)
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print_results_LT(v_theta, knot_description,
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ksi, untwisted_part,
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k, sigma_q_1, sigma_q_2, sigma_q_3)
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print_results_sigma(v_theta, knot_description, tp, q_4)
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print "*" * 100 + "\n" * 5
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print("*" * 100 + "\n" * 5)
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else:
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print knot_description + "\t" + str(v_theta) +\
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"\t" + str(sigma_v)
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print(knot_description + "\t" + str(v_theta) +\
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"\t" + str(sigma_v))
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if config.stop_after_firts_large_signature:
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break
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else:
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if config.print_calculations_for_small_signature:
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print "\n" * 5 + "*" * 100
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print "\nSmall signature value\n"
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print knot_description
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print("\n" * 5 + "*" * 100)
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print("\nSmall signature value\n")
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print(knot_description)
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print_results_LT(v_theta, knot_description, ksi, untwisted_part,
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k, sigma_q_1, sigma_q_2, sigma_q_3)
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print_results_sigma(v_theta, knot_description, tp, q_4)
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print "*" * 100 + "\n" * 5
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print("*" * 100 + "\n" * 5)
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else:
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print(knot_description + "\t" + str(v_theta) +\
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"\t" + str(sigma_v))
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large_sigma_for_all_v_comninations = False
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print("ojojojoj")
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break
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if large_sigma_for_all_v_comninations:
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print("\n\n\nHura hura")
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good_knots.append((knot_description, v_theta))
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# else:
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# print "\n\tSmall signature value"
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@ -331,18 +401,18 @@ def eval_cable_for_large_signature(k_vector=None,
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# print condition
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# print "non zero value in v_theta: " + str(np.count_nonzero(v_theta))
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# print "signature at 1/2: " + str(y)
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return None
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return good_knots
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def print_results_LT(v_theta, knot_description, ksi, untwisted_part,
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k, sigma_q_1, sigma_q_2, sigma_q_3):
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a_1, a_2, a_3, a_4 = v_theta
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k_1, k_2, k_3, k_4 = [abs(i) for i in k]
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print "\n\nLevine-Tristram signatures for the cable sum: "
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print knot_description
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print "and characters:\n" + str(v_theta) + ","
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print "ksi = " + str(ksi)
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print "\n\n2 * (sigma_q_2(ksi * a_1) + " + \
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print("\n\nLevine-Tristram signatures for the cable sum: ")
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print(knot_description)
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print("and characters:\n" + str(v_theta) + ",")
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print("ksi = " + str(ksi))
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print("\n\n2 * (sigma_q_2(ksi * a_1) + " + \
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"sigma_q_1(ksi * a_1 * 2) - " +\
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"sigma_q_2(ksi * a_2) + " +\
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"sigma_q_3(ksi * a_3) - " +\
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@ -376,71 +446,71 @@ def print_results_LT(v_theta, knot_description, ksi, untwisted_part,
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str(mod_one(ksi * a_4 * 2)) + \
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\
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") = \n\n2 * ((" + \
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str(sigma_q_2(mod_one(ksi * a_1))) + \
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str(sigma_q_2(ksi * a_1)) + \
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") + (" + \
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str(sigma_q_1(mod_one(ksi * a_1 * 2))) + \
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str(sigma_q_1(ksi * a_1 * 2)) + \
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") - (" + \
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str(sigma_q_2(mod_one(ksi * a_2))) + \
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str(sigma_q_2(ksi * a_2)) + \
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") + (" + \
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str(sigma_q_3(mod_one(ksi * a_3))) + \
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str(sigma_q_3(ksi * a_3)) + \
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") - (" + \
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str(sigma_q_3(mod_one(ksi * a_4))) + \
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str(sigma_q_3(ksi * a_4)) + \
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") - (" + \
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str(sigma_q_1(mod_one(ksi * a_4 * 2))) + ")) = " + \
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str(sigma_q_1(ksi * a_4 * 2)) + ")) = " + \
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"\n\n2 * (" + \
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str(sigma_q_2(mod_one(ksi * a_1)) +
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sigma_q_1(mod_one(ksi * a_1 * 2)) -
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sigma_q_2(mod_one(ksi * a_2)) +
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sigma_q_3(mod_one(ksi * a_3)) -
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sigma_q_3(mod_one(ksi * a_4)) -
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sigma_q_1(mod_one(ksi * a_4 * 2))) + \
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") = " + str(untwisted_part)
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print "\nSignatures:"
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print "\nq_1 = " + str(2 * k_1 + 1) + ": " + repr(sigma_q_1)
|
||||
print "\nq_2 = " + str(2 * k_2 + 1) + ": " + repr(sigma_q_2)
|
||||
print "\nq_3 = " + str(2 * k_3 + 1) + ": " + repr(sigma_q_3)
|
||||
str(sigma_q_2(ksi * a_1) +
|
||||
sigma_q_1(ksi * a_1 * 2) -
|
||||
sigma_q_2(ksi * a_2) +
|
||||
sigma_q_3(ksi * a_3) -
|
||||
sigma_q_3(ksi * a_4) -
|
||||
sigma_q_1(ksi * a_4 * 2)) + \
|
||||
") = " + str(untwisted_part))
|
||||
print("\nSignatures:")
|
||||
print("\nq_1 = " + str(2 * k_1 + 1) + ": " + repr(sigma_q_1))
|
||||
print("\nq_2 = " + str(2 * k_2 + 1) + ": " + repr(sigma_q_2))
|
||||
print("\nq_3 = " + str(2 * k_3 + 1) + ": " + repr(sigma_q_3))
|
||||
|
||||
|
||||
def print_results_sigma(v_theta, knot_description, tp, q_4):
|
||||
a_1, a_2, a_3, a_4 = v_theta
|
||||
|
||||
print "\n\nSigma values for the cable sum: "
|
||||
print knot_description
|
||||
print "and characters: " + str(v_theta)
|
||||
print "\nsigma(T_{2, q_4}, ksi_a) = " + \
|
||||
print("\n\nSigma values for the cable sum: ")
|
||||
print(knot_description)
|
||||
print("and characters: " + str(v_theta))
|
||||
print("\nsigma(T_{2, q_4}, ksi_a) = " + \
|
||||
"-q + (2 * a * (q_4 - a)/q_4) " +\
|
||||
"= -q + 2 * a - 2 * a^2/q_4 if a != 0,\n\t\t\t" +\
|
||||
" = 0 if a == 0."
|
||||
print "\nsigma(T_{2, q_4}, chi_a_1) = ",
|
||||
" = 0 if a == 0.")
|
||||
print("\nsigma(T_{2, q_4}, chi_a_1) = ", end="")
|
||||
if a_1:
|
||||
print "- (" + str(q_4) + ") + 2 * " + str(a_1) + " + " +\
|
||||
print("- (" + str(q_4) + ") + 2 * " + str(a_1) + " + " +\
|
||||
"- 2 * " + str(a_1^2) + "/" + str(q_4) + \
|
||||
" = " + str(tp[0])
|
||||
" = " + str(tp[0]))
|
||||
else:
|
||||
print "0"
|
||||
print "\nsigma(T_{2, q_4}, chi_a_2) = ",
|
||||
print("0")
|
||||
print("\nsigma(T_{2, q_4}, chi_a_2) = ", end ="")
|
||||
if a_2:
|
||||
print "- (" + str(q_4) + ") + 2 * " + str(a_2) + " + " +\
|
||||
print("- (" + str(q_4) + ") + 2 * " + str(a_2) + " + " +\
|
||||
"- 2 * " + str(a_2^2) + "/" + str(q_4) + \
|
||||
" = " + str(tp[1])
|
||||
" = " + str(tp[1]))
|
||||
else:
|
||||
print "0",
|
||||
print "\nsigma(T_{2, q_4}, chi_a_3) = ",
|
||||
print("0", end="")
|
||||
print("\nsigma(T_{2, q_4}, chi_a_3) = ", end="")
|
||||
if a_3:
|
||||
print "- (" + str(q_4) + ") + 2 * " + str(a_3) + " + " +\
|
||||
print("- (" + str(q_4) + ") + 2 * " + str(a_3) + " + " +\
|
||||
"- 2 * " + str(a_3^2) + "/" + str(q_4) + \
|
||||
" = " + str(tp[2])
|
||||
" = " + str(tp[2]))
|
||||
else:
|
||||
print "0",
|
||||
print "\nsigma(T_{2, q_4}, chi_a_4) = ",
|
||||
print("0", end="")
|
||||
print("\nsigma(T_{2, q_4}, chi_a_4) = ", end="")
|
||||
if a_4:
|
||||
print "- (" + str(q_4) + ") + 2 * " + str(a_4) + " + " +\
|
||||
print("- (" + str(q_4) + ") + 2 * " + str(a_4) + " + " +\
|
||||
"- 2 * " + str(a_4^2) + "/" + str(q_4) + \
|
||||
" = " + str(tp[3])
|
||||
" = " + str(tp[3]))
|
||||
else:
|
||||
print "0"
|
||||
print("0")
|
||||
|
||||
print "\n\nsigma(T_{2, q_4}, chi_a_1) " + \
|
||||
print("\n\nsigma(T_{2, q_4}, chi_a_1) " + \
|
||||
"- sigma(T_{2, q_4}, chi_a_2) " + \
|
||||
"+ sigma(T_{2, q_4}, chi_a_3) " + \
|
||||
"- sigma(T_{2, q_4}, chi_a_4) =\n" + \
|
||||
@ -448,7 +518,7 @@ def print_results_sigma(v_theta, knot_description, tp, q_4):
|
||||
") - sigma(T_{2, q_4}, " + str(a_2) + \
|
||||
") + sigma(T_{2, q_4}, " + str(a_3) + \
|
||||
") - sigma(T_{2, q_4}, " + str(a_4) + ") = " + \
|
||||
str(tp[0] - tp[1] + tp[2] - tp[3])
|
||||
str(tp[0] - tp[1] + tp[2] - tp[3]))
|
||||
|
||||
# searching for signature == 0
|
||||
def search_for_null_signature_value(knot_formula=None, limit=None):
|
||||
@ -468,7 +538,7 @@ def search_for_null_signature_value(knot_formula=None, limit=None):
|
||||
k = get_shifted_combination(k)
|
||||
knot_sum = eval(knot_formula)
|
||||
if is_trivial_combination(knot_sum):
|
||||
print knot_sum
|
||||
print(knot_sum)
|
||||
continue
|
||||
|
||||
result = eval_cable_for_null_signature(knot_sum)
|
||||
@ -492,8 +562,8 @@ def eval_cable_for_null_signature(knot_sum, print_results=False, verbose=None):
|
||||
|
||||
ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
|
||||
if verbose:
|
||||
print
|
||||
print knot_description
|
||||
print()
|
||||
print(knot_description)
|
||||
for v_theta in it.product(*ranges_list):
|
||||
if f(*v_theta, verbose=False).is_zero_everywhere():
|
||||
zero_theta_combinations.append(v_theta)
|
||||
@ -503,14 +573,14 @@ def eval_cable_for_null_signature(knot_sum, print_results=False, verbose=None):
|
||||
# assert sum(v_theta) != 0
|
||||
|
||||
if print_results:
|
||||
print
|
||||
print knot_description
|
||||
print "Zero cases: " + str(null_combinations)
|
||||
print "All cases: " + str(all_combinations)
|
||||
print()
|
||||
print(knot_description)
|
||||
print("Zero cases: " + str(null_combinations))
|
||||
print("All cases: " + str(all_combinations))
|
||||
if zero_theta_combinations:
|
||||
print "Zero theta combinations: "
|
||||
print("Zero theta combinations: ")
|
||||
for el in zero_theta_combinations:
|
||||
print el
|
||||
print(el)
|
||||
if null_combinations^2 >= all_combinations:
|
||||
return knot_description, null_combinations, all_combinations
|
||||
return None
|
||||
@ -553,12 +623,12 @@ def get_blanchfield_for_pattern(k_n, theta):
|
||||
results.append((1 - e * ksi, -1 * sgn(k_n)))
|
||||
|
||||
# lambda_even
|
||||
# print "normal"
|
||||
# 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"
|
||||
# print("reversed")
|
||||
for e in range(theta + 1, k + 1):
|
||||
if (theta + e) % 2 != 0:
|
||||
continue
|
||||
@ -637,13 +707,13 @@ def get_signature_as_theta_function(*arg, **key_args):
|
||||
sf += get_signature_summand_as_theta_function(*knot)(thetas[i])
|
||||
# in case wrong theata value was given
|
||||
except ValueError as e:
|
||||
print "ValueError: " + str(e.args[0]) +\
|
||||
" Please change " + str(i + 1) + ". parameter."
|
||||
print("ValueError: " + str(e.args[0]) +\
|
||||
" Please change " + str(i + 1) + ". parameter.")
|
||||
return None
|
||||
if verbose:
|
||||
print
|
||||
print str(thetas)
|
||||
print sf
|
||||
print()
|
||||
print(str(thetas))
|
||||
print(sf)
|
||||
return sf
|
||||
signature_as_theta_function.__doc__ = signature_as_theta_function_docstring
|
||||
return signature_as_theta_function
|
||||
@ -799,7 +869,7 @@ get_signature_as_theta_function.__doc__ = \
|
||||
sage: signature_function_generator = get_signature_as_theta_function(
|
||||
[1, 3], [2], [-1, -2], [-3])
|
||||
sage: sf = signature_function_generator(2, 1, 2, 2)
|
||||
sage: print sf
|
||||
sage: print(sf)
|
||||
0: 0
|
||||
5/42: 1
|
||||
1/7: 0
|
||||
@ -819,8 +889,8 @@ get_signature_as_theta_function.__doc__ = \
|
||||
37/42: -1
|
||||
|
||||
Or like below.
|
||||
sage: print get_signature_as_theta_function([1, 3], [2], [-1, -2], [-3]
|
||||
)(2, 1, 2, 2)
|
||||
sage: print(get_signature_as_theta_function([1, 3], [2], [-1, -2], [-3]
|
||||
)(2, 1, 2, 2))
|
||||
0: 0
|
||||
1/7: 0
|
||||
1/6: 0
|
||||
|
||||
Loading…
Reference in New Issue
Block a user